Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
480 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #26021390 | C2 | semidirect |
| 3. #26021352 | C2 | semidirect |
| 4. #26018077 | C2 | semidirect |
| 5. #26018077 | C2 | semidirect |
| 99. C2×D4×C89 | Q16 | semidirect |
| 212. C89 | #7782 | semidirect |
| 284. C2×D4 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028198 | 2 |
| #26021390 | 2 |
| #26021352 | 2 |
| #26018077 | 2 |
| #26018073 | 2 |
| C89×#2023 | 2 |
| #7782 | 89 |