Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
538 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#19151711 | C2 | semidirect |
| 3. C2×#19151412 | C2 | semidirect |
| 4. C2×#19151409 | C2 | semidirect |
| 5. #26021145 | C2 | semidirect |
| 6. #26018351 | C2 | semidirect |
| 7. C89×#1375 | C2 | semidirect |
| 13. C2×#15667957 | C4 | semidirect |
| 14. C2×D1424 | C4 | semidirect |
| 34. C2×Dic356 | C2×C4 | semidirect |
| 40. C2×D712 | C2×C4 | semidirect |
| 65. C2×C16×C89 | C2×C4 | semidirect |
| 185. #1375 | D89 | semidirect |
| 186. C89 | #13037 | semidirect |
| 237. C2×C16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152036 | 2 |
| C2×#19151711 | 2 |
| C2×#19151412 | 2 |
| C2×#19151409 | 2 |
| #26021145 | 2 |
| #26018351 | 2 |
| C89×#1375 | 2 |
| #13037 | 89 |