Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
1056 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 173 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 | C23×D89 |
| commutator, socle, cosocle | C23×C89 | C24 |
| Fitting | C22×C22⋊C4×C89 | C2 |
| hypercenter | C22×C22⋊C4 | D89 |
| hypocenter | C89 | #2404 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#13083574 | C2 | semidirect |
| 2. C2×#15667981 | C2 | semidirect |
| 3. #19151510 | C2 | semidirect |
| 4. #19151507 | C2 | semidirect |
| 5. #19151477 | C2 | semidirect |
| 6. #19151474 | C2 | semidirect |
| 7. #19151461 | C2 | semidirect |
| 8. C22×C22⋊C4×C89 | C2 | semidirect |
| 11. C22×Dic178 | C22 | semidirect |
| 12. C22×D356 | C22 | semidirect |
| 15. C22×C4×D89 | C22 | semidirect |
| 19. C2×#13083551 | C22 | semidirect |
| 20. #15667919 | C22 | semidirect |
| 21. #15667919 | C22 | semidirect |
| 22. #15667919 | C22 | semidirect |
| 40. C2×C22⋊D89 | D4 | semidirect |
| 58. C22×C4×C89 | D4 | semidirect |
| 76. C23×C89 | #41 | semidirect |
| 134. C89 | #2404 | semidirect |
| 137. C22×C22⋊C4 | D89 | semidirect |
| 189. C22×C4 | C22⋊D89 | semidirect |
| 215. C23 | #13083574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083574 | 2 |
| C2×#15667981 | 2 |
| #19151510 | 2 |
| #19151507 | 2 |
| #19151477 | 2 |
| #19151474 | 2 |
| #19151461 | 2 |
| C22×C22⋊C4×C89 | 2 |
| #2404 | 89 |