Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
412 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26021481 | C2 | semidirect |
| 2. #26019288 | C2 | semidirect |
| 4. #26018279 | C2 | semidirect |
| 5. #26018255 | C2 | semidirect |
| 6. #26018196 | C2 | semidirect |
| 7. C89×#2782 | C2 | semidirect |
| 192. #2782 | D89 | semidirect |
| 199. C89 | #12141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021481 | 2 |
| #26019288 | 2 |
| #26019186 | 2 |
| #26018279 | 2 |
| #26018255 | 2 |
| #26018196 | 2 |
| C89×#2782 | 2 |
| #12141 | 89 |