Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
1134 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 165 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 | #381×C89 | C2 |
| hypercenter | #381 | D89 |
| hypocenter | C89 | #2613 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D356 | C2 | semidirect |
| 2. C2×#15667995 | C2 | semidirect |
| 3. C2×#15667982 | C2 | semidirect |
| 4. #19151516 | C2 | semidirect |
| 5. #19151508 | C2 | semidirect |
| 6. #19151453 | C2 | semidirect |
| 7. #381×C89 | C2 | semidirect |
| 12. C22×D356 | C22 | semidirect |
| 16. C2×#13083553 | C22 | semidirect |
| 18. C2×#13083551 | C22 | semidirect |
| 19. C2×#13083551 | C22 | semidirect |
| 20. C2×#13083551 | C22 | semidirect |
| 23. #95×C89 | C22 | semidirect |
| 27. C23×D89 | D4 | semidirect |
| 46. C22×C4×C89 | D4 | semidirect |
| 104. C89 | #2613 | semidirect |
| 110. #381 | D89 | semidirect |
| 127. #95 | C2×D89 | semidirect |
| 145. C22×C4 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D356 | 2 |
| C2×#15667995 | 2 |
| C2×#15667982 | 2 |
| #19151516 | 2 |
| #19151508 | 2 |
| #19151453 | 2 |
| #381×C89 | 2 |
| #2613 | 89 |