Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19152033 | C2 | semidirect |
| 2. C2×#19151868 | C2 | semidirect |
| 3. C2×#19151405 | C2 | semidirect |
| 4. C2×#19151398 | C2 | semidirect |
| 5. C2×#19151382 | C2 | semidirect |
| 6. #26018360 | C2 | semidirect |
| 7. C89×#3061 | C2 | semidirect |
| 40. C2×D712 | D4 | semidirect |
| 46. #15667952 | D4 | semidirect |
| 52. #15667948 | D4 | semidirect |
| 221. #3061 | D89 | semidirect |
| 226. C89 | #13307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152033 | 2 |
| C2×#19151868 | 2 |
| C2×#19151405 | 2 |
| C2×#19151398 | 2 |
| C2×#19151382 | 2 |
| #26018360 | 2 |
| C89×#3061 | 2 |
| #13307 | 89 |