Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
498 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #26031450 | C2 | semidirect |
| 3. #26018886 | C2 | semidirect |
| 4. #26018725 | C2 | semidirect |
| 5. #26018593 | C2 | semidirect |
| 6. #26018113 | C2 | semidirect |
| 7. C89×#3110 | C2 | semidirect |
| 197. #3110 | D89 | semidirect |
| 203. C89 | #10042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031450 | 2 |
| #26030252 | 2 |
| #26018886 | 2 |
| #26018725 | 2 |
| #26018593 | 2 |
| #26018113 | 2 |
| C89×#3110 | 2 |
| #10042 | 89 |