Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 402 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. C2×#19151996 | C2 | semidirect |
| 3. #26018352 | C2 | semidirect |
| 4. #26018334 | C2 | semidirect |
| 31. C2×Q16×C89 | Q8 | semidirect |
| 33. C2×D8×C89 | Q8 | semidirect |
| 124. C89 | #13371 | semidirect |
| 140. C2×Q16 | Dic178 | semidirect |
| 142. C2×D8 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151996 | 2 |
| C2×#19151408 | 2 |
| #26018352 | 2 |
| #26018334 | 2 |
| C89×#1974 | 2 |
| #13371 | 89 |