Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
520 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26029972 | C2 | semidirect |
| 3. C2×#19151405 | C2 | semidirect |
| 4. C2×#19151404 | C2 | semidirect |
| 5. #26021866 | C2 | semidirect |
| 6. #26018355 | C2 | semidirect |
| 7. C89×#3067 | C2 | semidirect |
| 225. #3067 | D89 | semidirect |
| 230. C89 | #13312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033386 | 2 |
| #26029972 | 2 |
| C2×#19151405 | 2 |
| C2×#19151404 | 2 |
| #26021866 | 2 |
| #26018355 | 2 |
| C89×#3067 | 2 |
| #13312 | 89 |