Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
538 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26020319 | C2 | semidirect |
| 3. #26020009 | C2 | semidirect |
| 4. #26018078 | C2 | semidirect |
| 5. #26018072 | C2 | semidirect |
| 6. #26018072 | C2 | semidirect |
| 7. C89×#1272 | C2 | semidirect |
| 229. #1272 | D89 | semidirect |
| 232. C89 | #7670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028556 | 2 |
| #26020319 | 2 |
| #26020009 | 2 |
| #26018078 | 2 |
| #26018072 | 2 |
| C89×#1272 | 2 |
| #7670 | 89 |