Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
820 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 820 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. #26020718 | C2 | semidirect |
| 3. #26020716 | C2 | semidirect |
| 4. #26020547 | C2 | semidirect |
| 5. #26018615 | C2 | semidirect |
| 6. #26018588 | C2 | semidirect |
| 7. C89×#1471 | C2 | semidirect |
| 313. #1471 | D89 | semidirect |
| 315. C89 | #8538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034086 | 2 |
| #26020718 | 2 |
| #26020716 | 2 |
| #26020547 | 2 |
| #26018615 | 2 |
| #26018588 | 2 |
| C89×#1471 | 2 |
| #8538 | 89 |