Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
556 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 556 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 | #385×C89 | C2 |
| prime radical | #19151507 | C2 |
| hypercenter | #385 | D89 |
| hypocenter | C89 | #2712 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #385 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15667998 | C2 | semidirect |
| 2. #19151523 | C2 | semidirect |
| 3. #19151515 | C2 | semidirect |
| 4. #19151511 | C2 | semidirect |
| 6. #19151503 | C2 | semidirect |
| 7. #19151490 | C2 | semidirect |
| 8. #19151477 | C2 | semidirect |
| 9. #385×C89 | C2 | semidirect |
| 61. C22⋊C4×C89 | D4 | semidirect |
| 130. C89 | #2712 | semidirect |
| 139. #385 | D89 | semidirect |
| 190. C22⋊C4 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667998 | 2 |
| #19151523 | 2 |
| #19151515 | 2 |
| #19151511 | 2 |
| #19151507 | 2 |
| #19151503 | 2 |
| #19151490 | 2 |
| #19151477 | 2 |
| #385×C89 | 2 |
| #2712 | 89 |