Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26019000 | C2 | semidirect |
| 4. #26018110 | C2 | semidirect |
| 5. C89×#1835 | C2 | semidirect |
| 9. #19151677 | C4 | semidirect |
| 11. C8×D356 | C4 | semidirect |
| 136. #1835 | D89 | semidirect |
| 140. C89 | #8678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028965 | 2 |
| #26019000 | 2 |
| #26018811 | 2 |
| #26018110 | 2 |
| C89×#1835 | 2 |
| #8678 | 89 |