Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
534 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26021197 | C2 | semidirect |
| 5. #26018699 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 7. C89×#3113 | C2 | semidirect |
| 207. #3113 | D89 | semidirect |
| 213. C89 | #10010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031251 | 2 |
| #26025740 | 2 |
| #26021197 | 2 |
| #26018851 | 2 |
| #26018699 | 2 |
| #26018107 | 2 |
| C89×#3113 | 2 |
| #10010 | 89 |