Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
720 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26020018 | C2 | semidirect |
| 3. #26018873 | C2 | semidirect |
| 4. #26018710 | C2 | semidirect |
| 5. C89×#1464 | C2 | semidirect |
| 233. #1464 | D89 | semidirect |
| 234. C89 | #8349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033972 | 2 |
| #26020018 | 2 |
| #26018873 | 2 |
| #26018710 | 2 |
| C89×#1464 | 2 |
| #8349 | 89 |