Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
344 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 344 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. #26031723 | C2 | semidirect |
| 2. #26022203 | C2 | semidirect |
| 4. #26018239 | C2 | semidirect |
| 5. #26018236 | C2 | semidirect |
| 6. #26018205 | C2 | semidirect |
| 7. C89×#2053 | C2 | semidirect |
| 175. #2053 | D89 | semidirect |
| 179. C89 | #12172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031723 | 2 |
| #26022203 | 2 |
| #26022198 | 2 |
| #26018239 | 2 |
| #26018236 | 2 |
| #26018205 | 2 |
| C89×#2053 | 2 |
| #12172 | 89 |