Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
2070 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D71 |
| commutator, socle, cosocle | C23×C71 | C25 |
| Fitting | C71×#2840 | C2 |
| hypercenter | #2840 | D71 |
| hypocenter | C71 | #36675 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22596531 | C2 | semidirect |
| 2. #22596424 | C2 | semidirect |
| 3. #22596337 | C2 | semidirect |
| 4. #22591622 | C2 | semidirect |
| 5. #22591557 | C2 | semidirect |
| 6. #22590839 | C2 | semidirect |
| 7. C71×#2840 | C2 | semidirect |
| 8. C22×#11765866 | C22 | semidirect |
| 11. C2×Q8×Dic71 | C22 | semidirect |
| 13. #17985941 | C22 | semidirect |
| 14. #17985926 | C22 | semidirect |
| 16. #17985918 | C22 | semidirect |
| 17. #17985917 | C22 | semidirect |
| 19. #17985910 | C22 | semidirect |
| 24. #17985846 | C22 | semidirect |
| 25. #17985844 | C22 | semidirect |
| 76. C24×C71 | #41 | semidirect |
| 131. #2840 | D71 | semidirect |
| 138. C71 | #36675 | semidirect |
| 189. C24 | #11765866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596531 | 2 |
| #22596424 | 2 |
| #22596337 | 2 |
| #22591622 | 2 |
| #22591557 | 2 |
| #22590839 | 2 |
| C71×#2840 | 2 |
| #36675 | 71 |