Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
382 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | C2×#99 |
| commutator | C22×C4 | C22×C4×C89 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C89 |
| prime radical | C24×C89 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C22×C4×C89 ◁ C2×#117×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C2×#125×C89 | C4 | semidirect |
| 9. #400×C89 | C4 | semidirect |
| 11. #398×C89 | C4 | semidirect |
| 18. #376×C89 | C4 | semidirect |
| 154. #11846 | C89 | direct (N × H) |
| 166. C89 | #11846 | direct (N × H) |
| 167. C2×#125 | C4×C89 | semidirect |
| 170. #400 | C4×C89 | semidirect |
| 172. #398 | C4×C89 | semidirect |
| 179. #376 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2611 | 2 |
| C89×#1820 | 2 |
| C89×#1458 | 2 |
| C89×#1352 | 2 |
| C89×#1344 | 2 |
| #11846 | 89 |