Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
1168 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D89 |
| commutator | C23×C89 | C22×C4 |
| Fitting, prime radical | C23×D4×C89 | C2 |
| socle, cosocle | C24×C89 | C23 |
| hypercenter | C23×D4 | D89 |
| hypocenter | C89 | #1438 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊Dic89 | C2 | semidirect |
| 2. C2×#15667919 | C2 | semidirect |
| 11. C22×D4×C89 | C4 | semidirect |
| 17. C22×Dic89 | D4 | semidirect |
| 45. C23×C89 | C22⋊C4 | semidirect |
| 54. C2×C4×C89 | C22⋊C4 | semidirect |
| 85. C89 | #1438 | semidirect |
| 92. C22×D4 | Dic89 | semidirect |
| 130. C23 | C22⋊Dic89 | semidirect |
| 144. C2×C4 | C22⋊Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic89 | 2 |
| C2×#15667919 | 2 |
| C23×D4×C89 | 2 |
| #1438 | 89 |