Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
418 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26021811 | C2 | semidirect |
| 3. #26021723 | C2 | semidirect |
| 5. #26018076 | C2 | semidirect |
| 7. C89×#1271 | C2 | semidirect |
| 193. #1271 | D89 | semidirect |
| 195. C89 | #7788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027181 | 2 |
| #26021811 | 2 |
| #26021723 | 2 |
| #26021657 | 2 |
| #26018076 | 2 |
| #26018072 | 2 |
| C89×#1271 | 2 |
| #7788 | 89 |