Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
536 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26021393 | C2 | semidirect |
| 3. #26021389 | C2 | semidirect |
| 4. #26021337 | C2 | semidirect |
| 5. #26018072 | C2 | semidirect |
| 6. #26018072 | C2 | semidirect |
| 7. C89×#1272 | C2 | semidirect |
| 114. C2×Q8×C89 | SD16 | semidirect |
| 231. #1272 | D89 | semidirect |
| 234. C89 | #7781 | semidirect |
| 301. C2×Q8 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027278 | 2 |
| #26021393 | 2 |
| #26021389 | 2 |
| #26021337 | 2 |
| #26018072 | 2 |
| C89×#1272 | 2 |
| #7781 | 89 |