Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
396 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #26021728 | C2 | semidirect |
| 4. #26021662 | C2 | semidirect |
| 5. #26018077 | C2 | semidirect |
| 7. C89×#1271 | C2 | semidirect |
| 193. #1271 | D89 | semidirect |
| 195. C89 | #7820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028229 | 2 |
| #26021779 | 2 |
| #26021728 | 2 |
| #26021662 | 2 |
| #26018077 | 2 |
| #26018072 | 2 |
| C89×#1271 | 2 |
| #7820 | 89 |