Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
820 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 142 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 | #379 |
| commutator | C42 | C22×C4×C89 |
| Frattini, cosocle | C2×C42 | C23×C89 |
| prime radical | C89×#3549 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C2×C42×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C89×#1963 | C2 | semidirect |
| 3. C89×#1557 | C2 | semidirect |
| 4. C89×#1536 | C2 | semidirect |
| 5. C89×#1505 | C2 | semidirect |
| 8. #555×C89 | C4 | semidirect |
| 10. D42×C89 | C4 | semidirect |
| 15. #432×C89 | C22 | semidirect |
| 16. #423×C89 | C22 | semidirect |
| 18. #376×C89 | C22 | semidirect |
| 149. #8491 | C89 | direct (N × H) |
| 156. #1963 | C2×C89 | semidirect |
| 157. #1557 | C2×C89 | semidirect |
| 158. #1536 | C2×C89 | semidirect |
| 159. #1505 | C2×C89 | semidirect |
| 160. C89 | #8491 | direct (N × H) |
| 163. #555 | C4×C89 | semidirect |
| 165. D42 | C4×C89 | semidirect |
| 170. #432 | C22×C89 | semidirect |
| 171. #423 | C22×C89 | semidirect |
| 173. #376 | C22×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3549 | 2 |
| C89×#1963 | 2 |
| C89×#1557 | 2 |
| C89×#1536 | 2 |
| C89×#1505 | 2 |
| #8491 | 89 |