Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
312 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26033121 | C2 | semidirect |
| 3. #26019609 | C2 | semidirect |
| 4. #26018310 | C2 | semidirect |
| 5. #26018232 | C2 | semidirect |
| 6. #26018214 | C2 | semidirect |
| 7. C89×#2240 | C2 | semidirect |
| 59. D712 | SD16 | semidirect |
| 134. #2240 | D89 | semidirect |
| 140. C89 | #12355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033121 | 2 |
| #26022284 | 2 |
| #26019609 | 2 |
| #26018310 | 2 |
| #26018232 | 2 |
| #26018214 | 2 |
| C89×#2240 | 2 |
| #12355 | 89 |