Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1092 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 147 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. #26021093 | C2 | semidirect |
| 2. #26018987 | C2 | semidirect |
| 3. #26018844 | C2 | semidirect |
| 4. #26018691 | C2 | semidirect |
| 6. #19151622 | C22 | semidirect |
| 8. C4×#13083558 | C22 | semidirect |
| 134. Q8×C89 | #100 | semidirect |
| 150. D4×C89 | #100 | semidirect |
| 202. C89 | #8469 | semidirect |
| 331. Q8 | #15667929 | semidirect |
| 347. D4 | #15667929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021093 | 2 |
| #26018987 | 2 |
| #26018844 | 2 |
| #26018691 | 2 |
| C89×#3498 | 2 |
| #8469 | 89 |