Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
502 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26021028 | C2 | semidirect |
| 3. #26018927 | C2 | semidirect |
| 4. #26018920 | C2 | semidirect |
| 5. #26018650 | C2 | semidirect |
| 6. #26018102 | C2 | semidirect |
| 7. C2×#331×C89 | C2 | semidirect |
| 204. C2×#331 | D89 | semidirect |
| 207. C89 | #10549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030702 | 2 |
| #26021028 | 2 |
| #26018927 | 2 |
| #26018920 | 2 |
| #26018650 | 2 |
| #26018102 | 2 |
| C2×#331×C89 | 2 |
| #10549 | 89 |