Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
794 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26021047 | C2 | semidirect |
| 3. #26018640 | C2 | semidirect |
| 4. #26018632 | C2 | semidirect |
| 5. C89×#1460 | C2 | semidirect |
| 198. #1460 | D89 | semidirect |
| 199. C89 | #8320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033674 | 2 |
| #26021047 | 2 |
| #26018640 | 2 |
| #26018632 | 2 |
| C89×#1460 | 2 |
| #8320 | 89 |