Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26029137 | C2 | semidirect |
| 3. #26021987 | C2 | semidirect |
| 4. C2×#19151408 | C2 | semidirect |
| 5. #26018357 | C2 | semidirect |
| 6. #26018338 | C2 | semidirect |
| 7. C89×#1976 | C2 | semidirect |
| 10. #19152039 | C4 | semidirect |
| 12. #19152034 | C4 | semidirect |
| 50. #15667952 | C2×C4 | semidirect |
| 62. C2×Q16×C89 | C2×C4 | semidirect |
| 64. C2×D8×C89 | C2×C4 | semidirect |
| 194. #1976 | D89 | semidirect |
| 197. C89 | #13030 | semidirect |
| 230. C2×Q16 | C4×D89 | semidirect |
| 234. C2×D8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033386 | 2 |
| #26029137 | 2 |
| #26021987 | 2 |
| C2×#19151408 | 2 |
| #26018357 | 2 |
| #26018338 | 2 |
| C89×#1976 | 2 |
| #13030 | 89 |