Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 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 |
|---|---|---|
| 3. #26018816 | C2 | semidirect |
| 5. #26018647 | C2 | semidirect |
| 6. #26018112 | C2 | semidirect |
| 7. C89×#3078 | C2 | semidirect |
| 115. C2×Q8×C89 | SD16 | semidirect |
| 226. #3078 | D89 | semidirect |
| 232. C89 | #10001 | semidirect |
| 317. C2×Q8 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030256 | 2 |
| #26025157 | 2 |
| #26018816 | 2 |
| #26018676 | 2 |
| #26018647 | 2 |
| #26018112 | 2 |
| C89×#3078 | 2 |
| #10001 | 89 |