Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
550 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26020275 | C2 | semidirect |
| 4. #26018120 | C2 | semidirect |
| 5. C89×#1289 | C2 | semidirect |
| 7. C22×C8×D89 | C4 | semidirect |
| 12. C2×#15667941 | C4 | semidirect |
| 14. C2×#15667924 | C4 | semidirect |
| 15. C2×C8×Dic89 | C4 | semidirect |
| 111. C22×D89 | #106 | semidirect |
| 135. C2×Dic89 | #106 | semidirect |
| 143. #10623494 | #99 | semidirect |
| 183. #1289 | D89 | semidirect |
| 184. C89 | #8608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151661 | 2 |
| #26020275 | 2 |
| #26020237 | 2 |
| #26018120 | 2 |
| C89×#1289 | 2 |
| #8608 | 89 |