Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26028912 | C2 | semidirect |
| 3. #26020349 | C2 | semidirect |
| 6. #26018099 | C2 | semidirect |
| 7. C89×#1293 | C2 | semidirect |
| 17. C2×#15667946 | C4 | semidirect |
| 18. C2×#15667944 | C4 | semidirect |
| 20. C2×#15667934 | C4 | semidirect |
| 21. C2×#15667934 | C4 | semidirect |
| 229. #1293 | D89 | semidirect |
| 231. C89 | #9242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151923 | 2 |
| #26028912 | 2 |
| #26020349 | 2 |
| #26018769 | 2 |
| #26018613 | 2 |
| #26018099 | 2 |
| C89×#1293 | 2 |
| #9242 | 89 |