Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
490 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 77 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. #26020713 | C2 | semidirect |
| 3. #26020688 | C2 | semidirect |
| 4. #26020456 | C2 | semidirect |
| 5. #26018819 | C2 | semidirect |
| 6. #26018613 | C2 | semidirect |
| 7. C89×#1305 | C2 | semidirect |
| 231. #1305 | D89 | semidirect |
| 232. C89 | #10560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031052 | 2 |
| #26020713 | 2 |
| #26020688 | 2 |
| #26020456 | 2 |
| #26018819 | 2 |
| #26018613 | 2 |
| C89×#1305 | 2 |
| #10560 | 89 |