Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
578 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 133 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 | C2×#123×C89 | C2 |
| hypercenter | C2×#123 | D89 |
| hypocenter | C89 | #2813 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×#123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15667986 | C2 | semidirect |
| 2. #19151537 | C2 | semidirect |
| 3. #19151534 | C2 | semidirect |
| 4. #19151520 | C2 | semidirect |
| 5. #19151515 | C2 | semidirect |
| 6. #19151514 | C2 | semidirect |
| 7. #19151513 | C2 | semidirect |
| 8. #19151507 | C2 | semidirect |
| 9. #19151506 | C2 | semidirect |
| 10. #19151458 | C2 | semidirect |
| 11. C2×#123×C89 | C2 | semidirect |
| 63. C22×C4×C89 | D4 | semidirect |
| 156. C89 | #2813 | semidirect |
| 157. C2×#123 | D89 | semidirect |
| 210. C22×C4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667986 | 2 |
| #19151537 | 2 |
| #19151534 | 2 |
| #19151520 | 2 |
| #19151515 | 2 |
| #19151514 | 2 |
| #19151513 | 2 |
| #19151507 | 2 |
| #19151506 | 2 |
| #19151458 | 2 |
| C2×#123×C89 | 2 |
| #2813 | 89 |