Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
492 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 137 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 | #391×C89 | C2 |
| prime radical | C22×D356 | C22 |
| hypercenter | #391 | D89 |
| hypocenter | C89 | #2731 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15668010 | C2 | semidirect |
| 3. #19151520 | C2 | semidirect |
| 5. #19151511 | C2 | semidirect |
| 6. #19151490 | C2 | semidirect |
| 7. #19151489 | C2 | semidirect |
| 8. #19151483 | C2 | semidirect |
| 9. #391×C89 | C2 | semidirect |
| 126. C89 | #2731 | semidirect |
| 132. #391 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668010 | 2 |
| C2×#15668001 | 2 |
| #19151520 | 2 |
| #19151516 | 2 |
| #19151511 | 2 |
| #19151490 | 2 |
| #19151489 | 2 |
| #19151483 | 2 |
| #391×C89 | 2 |
| #2731 | 89 |