Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
550 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26031382 | C2 | semidirect |
| 3. #26030645 | C2 | semidirect |
| 4. #26021175 | C2 | semidirect |
| 5. #26021170 | C2 | semidirect |
| 6. #26018101 | C2 | semidirect |
| 7. C89×#1502 | C2 | semidirect |
| 206. #1502 | D89 | semidirect |
| 208. C89 | #10200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031559 | 2 |
| #26031382 | 2 |
| #26030645 | 2 |
| #26021175 | 2 |
| #26021170 | 2 |
| #26018101 | 2 |
| C89×#1502 | 2 |
| #10200 | 89 |