Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
724 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 151 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 | #392×C89 | C2 |
| hypercenter | #392 | D89 |
| hypocenter | C89 | #2543 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15667983 | C2 | semidirect |
| 2. C2×#15667983 | C2 | semidirect |
| 3. C2×#15667972 | C2 | semidirect |
| 4. #19151530 | C2 | semidirect |
| 5. #19151523 | C2 | semidirect |
| 6. #19151512 | C2 | semidirect |
| 7. #19151491 | C2 | semidirect |
| 8. #19151478 | C2 | semidirect |
| 9. #19151474 | C2 | semidirect |
| 10. #95×D89 | C2 | semidirect |
| 11. #392×C89 | C2 | semidirect |
| 44. C2×C22⋊D89 | D4 | semidirect |
| 56. C2×C4×D89 | D4 | semidirect |
| 162. C89 | #2543 | semidirect |
| 169. #392 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667983 | 2 |
| C2×#15667972 | 2 |
| #19151530 | 2 |
| #19151523 | 2 |
| #19151512 | 2 |
| #19151491 | 2 |
| #19151478 | 2 |
| #19151474 | 2 |
| #95×D89 | 2 |
| #392×C89 | 2 |
| #2543 | 89 |