Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
770 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26031239 | C2 | semidirect |
| 2. #26030702 | C2 | semidirect |
| 3. #26018966 | C2 | semidirect |
| 4. #26018850 | C2 | semidirect |
| 5. #26018759 | C2 | semidirect |
| 6. #26018145 | C2 | semidirect |
| 7. C89×#2657 | C2 | semidirect |
| 38. #15668012 | D4 | semidirect |
| 39. #15668009 | D4 | semidirect |
| 46. C4⋊#10623494 | D4 | semidirect |
| 53. #15667923 | D4 | semidirect |
| 214. #2657 | D89 | semidirect |
| 219. C89 | #10088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031239 | 2 |
| #26030702 | 2 |
| #26018966 | 2 |
| #26018850 | 2 |
| #26018759 | 2 |
| #26018145 | 2 |
| C89×#2657 | 2 |
| #10088 | 89 |