Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1170 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1170 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. #26031373 | C2 | semidirect |
| 3. #26019254 | C2 | semidirect |
| 4. #26018746 | C2 | semidirect |
| 5. #26018576 | C2 | semidirect |
| 6. C89×#2546 | C2 | semidirect |
| 185. #2546 | D89 | semidirect |
| 189. C89 | #18408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034023 | 2 |
| #26031373 | 2 |
| #26019254 | 2 |
| #26018746 | 2 |
| #26018576 | 2 |
| C89×#2546 | 2 |
| #18408 | 89 |