Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
360 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26021572 | C2 | semidirect |
| 4. #26018264 | C2 | semidirect |
| 6. #26018191 | C2 | semidirect |
| 7. C89×#2188 | C2 | semidirect |
| 169. #2188 | D89 | semidirect |
| 175. C89 | #12163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031605 | 2 |
| #26022169 | 2 |
| #26021572 | 2 |
| #26018264 | 2 |
| #26018262 | 2 |
| #26018191 | 2 |
| C89×#2188 | 2 |
| #12163 | 89 |