Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1174 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 191 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. #26031177 | C2 | semidirect |
| 3. #26019220 | C2 | semidirect |
| 4. #26018746 | C2 | semidirect |
| 5. #26018576 | C2 | semidirect |
| 6. C89×#2567 | C2 | semidirect |
| 102. C2×Q8×C89 | SD16 | semidirect |
| 183. #2567 | D89 | semidirect |
| 187. C89 | #18402 | semidirect |
| 267. C2×Q8 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034023 | 2 |
| #26031177 | 2 |
| #26019220 | 2 |
| #26018746 | 2 |
| #26018576 | 2 |
| C89×#2567 | 2 |
| #18402 | 89 |