Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
622 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. #26025157 | C2 | semidirect |
| 3. #26018812 | C2 | semidirect |
| 4. #26018676 | C2 | semidirect |
| 5. #26018647 | C2 | semidirect |
| 6. #26018112 | C2 | semidirect |
| 7. C89×#3037 | C2 | semidirect |
| 120. C2×Q8×C89 | D8 | semidirect |
| 245. #3037 | D89 | semidirect |
| 251. C89 | #9997 | semidirect |
| 341. C2×Q8 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030248 | 2 |
| #26025157 | 2 |
| #26018812 | 2 |
| #26018676 | 2 |
| #26018647 | 2 |
| #26018112 | 2 |
| C89×#3037 | 2 |
| #9997 | 89 |