Finite Group DatabasebetaFinite Group DatabasebetaOrder 36928.
250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D577 |
| commutator, socle, cosocle | C22×C577 | C24 |
| Fitting | #121×C577 | C2 |
| hypercenter | #121 | D577 |
| hypocenter | C577 | #538 |
| LCS | G ▷ C22×C577 ▷ C577 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #32914659 | C2 | semidirect |
| 2. #32914657 | C2 | semidirect |
| 3. #32914651 | C2 | semidirect |
| 4. #32914650 | C2 | semidirect |
| 5. #32914647 | C2 | semidirect |
| 6. #32914645 | C2 | semidirect |
| 7. #32914642 | C2 | semidirect |
| 8. #32914636 | C2 | semidirect |
| 9. #32914635 | C2 | semidirect |
| 10. #32914632 | C2 | semidirect |
| 11. #32914632 | C2 | semidirect |
| 12. C4×C22⋊D577 | C2 | semidirect |
| 13. #32914624 | C2 | semidirect |
| 14. C22⋊C4×D577 | C2 | semidirect |
| 15. #121×C577 | C2 | semidirect |
| 17. C2×Dic1154 | C22 | semidirect |
| 22. C22×Dic577 | C22 | semidirect |
| 25. C4⋊Dic577 | C22 | semidirect |
| 26. #22604397 | C22 | semidirect |
| 27. #22604397 | C22 | semidirect |
| 28. #22604397 | C22 | semidirect |
| 29. #22604397 | C22 | semidirect |
| 33. C22⋊Dic577 | C22 | semidirect |
| 34. C22⋊Dic577 | C22 | semidirect |
| 35. C22⋊Dic577 | C22 | semidirect |
| 42. C4×Dic577 | C22 | semidirect |
| 43. C4×Dic577 | C22 | semidirect |
| 46. C2×D4×C577 | C22 | semidirect |
| 47. C22×C4×C577 | C22 | semidirect |
| 48. C4⋊C4×C577 | C22 | semidirect |
| 50. C22⋊C4×C577 | C22 | semidirect |
| 116. C577 | #538 | semidirect |
| 127. #121 | D577 | semidirect |
| 141. C2×D4 | C2×D577 | semidirect |
| 145. C22×C4 | C2×D577 | semidirect |
| 151. C4⋊C4 | C2×D577 | semidirect |
| 165. C22⋊C4 | C2×D577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #32914659 | 2 |
| #32914657 | 2 |
| #32914651 | 2 |
| #32914650 | 2 |
| #32914647 | 2 |
| #32914645 | 2 |
| #32914642 | 2 |
| #32914636 | 2 |
| #32914635 | 2 |
| #32914632 | 2 |
| C4×C22⋊D577 | 2 |
| #32914624 | 2 |
| C22⋊C4×D577 | 2 |
| #121×C577 | 2 |
| #538 | 577 |