Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
428 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 3. #26018846 | C2 | semidirect |
| 4. #26018708 | C2 | semidirect |
| 6. #26018143 | C2 | semidirect |
| 7. C89×#1278 | C2 | semidirect |
| 198. #1278 | D89 | semidirect |
| 199. C89 | #9214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030324 | 2 |
| #26028894 | 2 |
| #26018846 | 2 |
| #26018708 | 2 |
| #26018692 | 2 |
| #26018143 | 2 |
| C89×#1278 | 2 |
| #9214 | 89 |