Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
622 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26031239 | C2 | semidirect |
| 2. #26031170 | C2 | semidirect |
| 3. #26018966 | C2 | semidirect |
| 4. #26018862 | C2 | semidirect |
| 5. #26018604 | C2 | semidirect |
| 6. #26018151 | C2 | semidirect |
| 7. C2×#496×C89 | C2 | semidirect |
| 204. C2×#496 | D89 | semidirect |
| 209. C89 | #10128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031239 | 2 |
| #26031170 | 2 |
| #26018966 | 2 |
| #26018862 | 2 |
| #26018604 | 2 |
| #26018151 | 2 |
| C2×#496×C89 | 2 |
| #10128 | 89 |