Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
424 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. #26028399 | C2 | semidirect |
| 3. #26019221 | C2 | semidirect |
| 4. #26018283 | C2 | semidirect |
| 5. #26018258 | C2 | semidirect |
| 6. #26018183 | C2 | semidirect |
| 7. C89×#1610 | C2 | semidirect |
| 200. #1610 | D89 | semidirect |
| 205. C89 | #12200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028399 | 2 |
| #26021294 | 2 |
| #26019221 | 2 |
| #26018283 | 2 |
| #26018258 | 2 |
| #26018183 | 2 |
| C89×#1610 | 2 |
| #12200 | 89 |