Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. C2×#19151995 | C2 | semidirect |
| 4. #26018351 | C2 | semidirect |
| 5. #26018350 | C2 | semidirect |
| 6. #26018333 | C2 | semidirect |
| 48. C2×Q16×C89 | Q8 | semidirect |
| 50. C2×D8×C89 | Q8 | semidirect |
| 156. C89 | #13371 | semidirect |
| 178. C2×Q16 | Dic178 | semidirect |
| 180. C2×D8 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151995 | 2 |
| C2×#19151408 | 2 |
| #26021141 | 2 |
| #26018351 | 2 |
| #26018350 | 2 |
| #26018333 | 2 |
| C2×#360×C89 | 2 |
| #13371 | 89 |