Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
604 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 604 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. #26027270 | C2 | semidirect |
| 2. #26021487 | C2 | semidirect |
| 3. #26021339 | C2 | semidirect |
| 5. #26018074 | C2 | semidirect |
| 6. #26018072 | C2 | semidirect |
| 7. C89×#1272 | C2 | semidirect |
| 90. C2×D356 | SD16 | semidirect |
| 121. C2×Q8×C89 | D8 | semidirect |
| 243. #1272 | D89 | semidirect |
| 246. C89 | #7735 | semidirect |
| 311. C2×Q8 | D712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027270 | 2 |
| #26021487 | 2 |
| #26021339 | 2 |
| #26021325 | 2 |
| #26018074 | 2 |
| #26018072 | 2 |
| C89×#1272 | 2 |
| #7735 | 89 |