Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
696 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 145 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 | #390×C89 | C2 |
| hypercenter | #390 | D89 |
| hypocenter | C89 | #2555 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15667998 | C2 | semidirect |
| 2. C2×#15667985 | C2 | semidirect |
| 3. #19151518 | C2 | semidirect |
| 4. #19151515 | C2 | semidirect |
| 5. #19151506 | C2 | semidirect |
| 6. #19151486 | C2 | semidirect |
| 7. #19151474 | C2 | semidirect |
| 8. C4×#13083551 | C2 | semidirect |
| 9. #390×C89 | C2 | semidirect |
| 55. #13083551 | D4 | semidirect |
| 143. C89 | #2555 | semidirect |
| 149. #390 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667998 | 2 |
| C2×#15667985 | 2 |
| #19151518 | 2 |
| #19151515 | 2 |
| #19151506 | 2 |
| #19151486 | 2 |
| #19151474 | 2 |
| C4×#13083551 | 2 |
| #390×C89 | 2 |
| #2555 | 89 |