Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
478 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26021656 | C2 | semidirect |
| 3. #26018078 | C2 | semidirect |
| 4. #26018072 | C2 | semidirect |
| 5. C89×#2096 | C2 | semidirect |
| 144. #2096 | D89 | semidirect |
| 148. C89 | #7810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027278 | 2 |
| #26021656 | 2 |
| #26018078 | 2 |
| #26018072 | 2 |
| C89×#2096 | 2 |
| #7810 | 89 |