Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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×D293 |
| commutator, socle, cosocle | C22×C293 | C24 |
| Fitting | C2×C22⋊C4×C293 | C2 |
| hypercenter | C2×C22⋊C4 | D293 |
| hypocenter | C293 | #538 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22627617 | C2 | semidirect |
| 2. #22627610 | C2 | semidirect |
| 3. #22627606 | C2 | semidirect |
| 4. #22627603 | C2 | semidirect |
| 5. #22627598 | C2 | semidirect |
| 6. #22627597 | C2 | semidirect |
| 7. #22627593 | C2 | semidirect |
| 8. C4×C22⋊D293 | C2 | semidirect |
| 9. C2×C22⋊C4×C293 | C2 | semidirect |
| 10. C2×Dic586 | C22 | semidirect |
| 11. C2×D1172 | C22 | semidirect |
| 15. C2×C4×D293 | C22 | semidirect |
| 16. C4⋊Dic293 | C22 | semidirect |
| 17. C4⋊Dic293 | C22 | semidirect |
| 18. #17989781 | C22 | semidirect |
| 19. #17989781 | C22 | semidirect |
| 23. #17989779 | C22 | semidirect |
| 24. #17989779 | C22 | semidirect |
| 25. C4×Dic293 | C22 | semidirect |
| 74. C293 | #538 | semidirect |
| 84. C2×C22⋊C4 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627617 | 2 |
| #22627610 | 2 |
| #22627606 | 2 |
| #22627603 | 2 |
| #22627598 | 2 |
| #22627597 | 2 |
| #22627593 | 2 |
| C4×C22⋊D293 | 2 |
| C2×C22⋊C4×C293 | 2 |
| #538 | 293 |