Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
578 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26031235 | C2 | semidirect |
| 2. #26030720 | C2 | semidirect |
| 3. #26018721 | C2 | semidirect |
| 4. #26018669 | C2 | semidirect |
| 5. #26018605 | C2 | semidirect |
| 6. #26018125 | C2 | semidirect |
| 7. C89×#3214 | C2 | semidirect |
| 213. #3214 | D89 | semidirect |
| 220. C89 | #10120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031235 | 2 |
| #26030720 | 2 |
| #26018721 | 2 |
| #26018669 | 2 |
| #26018605 | 2 |
| #26018125 | 2 |
| C89×#3214 | 2 |
| #10120 | 89 |