Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
592 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 157 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 | #386×C89 | C2 |
| prime radical | C22×D4×C89 | C22 |
| hypercenter | #386 | D89 |
| hypocenter | C89 | #2683 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15667991 | C2 | semidirect |
| 2. C2×#15667989 | C2 | semidirect |
| 3. #19151521 | C2 | semidirect |
| 4. #19151521 | C2 | semidirect |
| 5. #19151519 | C2 | semidirect |
| 7. #19151495 | C2 | semidirect |
| 48. #13083553 | D4 | semidirect |
| 58. C2×D4×C89 | Q8 | semidirect |
| 132. C89 | #2683 | semidirect |
| 172. C2×D4 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667991 | 2 |
| C2×#15667989 | 2 |
| #19151521 | 2 |
| #19151519 | 2 |
| #19151501 | 2 |
| #19151495 | 2 |
| #19151478 | 2 |
| #386×C89 | 2 |
| #2683 | 89 |