Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
900 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #26018130 | C2 | semidirect |
| 4. #26018095 | C2 | semidirect |
| 5. C89×#2659 | C2 | semidirect |
| 25. C22×D356 | Q8 | semidirect |
| 261. #2659 | D89 | semidirect |
| 266. C89 | #10340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020182 | 2 |
| #26018492 | 2 |
| #26018130 | 2 |
| #26018095 | 2 |
| C89×#2659 | 2 |
| #10340 | 89 |