Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26033386 | C2 | semidirect |
| 2. #26030698 | C2 | semidirect |
| 3. #26021979 | C2 | semidirect |
| 4. #26018332 | C2 | semidirect |
| 5. C89×#1975 | C2 | semidirect |
| 47. C2×#13083549 | D4 | semidirect |
| 51. C2×Q16×C89 | D4 | semidirect |
| 53. C2×D8×C89 | D4 | semidirect |
| 167. #1975 | D89 | semidirect |
| 169. C89 | #13340 | semidirect |
| 199. C2×Q16 | D356 | semidirect |
| 205. C2×D8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033386 | 2 |
| #26030698 | 2 |
| #26021979 | 2 |
| #26018332 | 2 |
| C89×#1975 | 2 |
| #13340 | 89 |