Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
674 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26021486 | C2 | semidirect |
| 2. #26021322 | C2 | semidirect |
| 3. #26021322 | C2 | semidirect |
| 4. #26018075 | C2 | semidirect |
| 5. #26018073 | C2 | semidirect |
| 6. #26018073 | C2 | semidirect |
| 7. C89×#2682 | C2 | semidirect |
| 114. C2×D4×C89 | D8 | semidirect |
| 132. C4⋊C4×C89 | D8 | semidirect |
| 262. #2682 | D89 | semidirect |
| 269. C89 | #7737 | semidirect |
| 365. C2×D4 | #13083559 | semidirect |
| 394. C4⋊C4 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021486 | 2 |
| #26021322 | 2 |
| #26018075 | 2 |
| #26018073 | 2 |
| C89×#2682 | 2 |
| #7737 | 89 |