Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
488 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#19151367 | C2 | semidirect |
| 3. #26018280 | C2 | semidirect |
| 4. #26018256 | C2 | semidirect |
| 5. C89×#1463 | C2 | semidirect |
| 198. #1463 | D89 | semidirect |
| 201. C89 | #11766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025732 | 2 |
| C2×#19151367 | 2 |
| #26018280 | 2 |
| #26018256 | 2 |
| C89×#1463 | 2 |
| #11766 | 89 |