Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
398 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 4. #26018145 | C2 | semidirect |
| 5. #26018116 | C2 | semidirect |
| 6. #26018108 | C2 | semidirect |
| 7. C89×#2605 | C2 | semidirect |
| 29. #15668012 | Q8 | semidirect |
| 30. #15668009 | Q8 | semidirect |
| 182. #2605 | D89 | semidirect |
| 189. C89 | #10378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021170 | 2 |
| #26018798 | 2 |
| #26018759 | 2 |
| #26018145 | 2 |
| #26018116 | 2 |
| #26018108 | 2 |
| C89×#2605 | 2 |
| #10378 | 89 |