Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
932 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 153 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 | #2615 |
| 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. C22×#13083573 | C2 | semidirect |
| 2. C2×#15667985 | C2 | semidirect |
| 3. C2×#15667984 | C2 | semidirect |
| 4. #19151511 | C2 | semidirect |
| 5. #19151510 | C2 | semidirect |
| 6. #19151507 | C2 | semidirect |
| 7. #19151506 | C2 | semidirect |
| 8. #19151506 | C2 | semidirect |
| 9. #19151457 | C2 | semidirect |
| 10. #19151456 | C2 | semidirect |
| 11. #392×C89 | C2 | semidirect |
| 58. C22×Dic89 | D4 | semidirect |
| 64. C2×C4×D89 | D4 | semidirect |
| 178. C89 | #2615 | semidirect |
| 187. #392 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083573 | 2 |
| C2×#15667985 | 2 |
| C2×#15667984 | 2 |
| #19151511 | 2 |
| #19151510 | 2 |
| #19151507 | 2 |
| #19151506 | 2 |
| #19151457 | 2 |
| #19151456 | 2 |
| #392×C89 | 2 |
| #2615 | 89 |