Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
556 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26020320 | C2 | semidirect |
| 3. #26018074 | C2 | semidirect |
| 4. #26018072 | C2 | semidirect |
| 5. C89×#1728 | C2 | semidirect |
| 199. #1728 | D89 | semidirect |
| 202. C89 | #7694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028583 | 2 |
| #26020320 | 2 |
| #26018074 | 2 |
| #26018072 | 2 |
| C89×#1728 | 2 |
| #7694 | 89 |