Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
488 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 165 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×#117×C89 | C2 |
| prime radical | C24×C89 | C23 |
| hypercenter | C2×#117 | D89 |
| hypocenter | C89 | #2628 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15668012 | C2 | semidirect |
| 2. #19151537 | C2 | semidirect |
| 4. #19151518 | C2 | semidirect |
| 6. #19151496 | C2 | semidirect |
| 7. #19151464 | C2 | semidirect |
| 41. C22×C4×C89 | Q8 | semidirect |
| 107. C89 | #2628 | semidirect |
| 143. C22×C4 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668012 | 2 |
| #19151537 | 2 |
| #19151534 | 2 |
| #19151518 | 2 |
| #19151510 | 2 |
| #19151496 | 2 |
| #19151464 | 2 |
| #19151458 | 2 |
| C2×#117×C89 | 2 |
| #2628 | 89 |