Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
612 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26021339 | C2 | semidirect |
| 3. #26018078 | C2 | semidirect |
| 4. #26018073 | C2 | semidirect |
| 5. C89×#2804 | C2 | semidirect |
| 75. C2×D4×C89 | SD16 | semidirect |
| 163. #2804 | D89 | semidirect |
| 168. C89 | #7745 | semidirect |
| 230. C2×D4 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021339 | 2 |
| #26021322 | 2 |
| #26018078 | 2 |
| #26018073 | 2 |
| C89×#2804 | 2 |
| #7745 | 89 |