Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
532 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 532 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. #26020232 | C2 | semidirect |
| 3. #26018076 | C2 | semidirect |
| 4. #26018072 | C2 | semidirect |
| 5. C89×#1749 | C2 | semidirect |
| 198. #1749 | D89 | semidirect |
| 201. C89 | #7698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028583 | 2 |
| #26020232 | 2 |
| #26018076 | 2 |
| #26018072 | 2 |
| C89×#1749 | 2 |
| #7698 | 89 |