Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
434 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 3. #26021729 | C2 | semidirect |
| 4. #26018075 | C2 | semidirect |
| 5. #26018074 | C2 | semidirect |
| 7. C89×#2084 | C2 | semidirect |
| 194. #2084 | D89 | semidirect |
| 198. C89 | #7819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027181 | 2 |
| #26021781 | 2 |
| #26021729 | 2 |
| #26018075 | 2 |
| #26018074 | 2 |
| #26018072 | 2 |
| C89×#2084 | 2 |
| #7819 | 89 |