Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26022488 | C2 | semidirect |
| 2. #26022404 | C2 | semidirect |
| 3. #26019765 | C2 | semidirect |
| 4. #26018295 | C2 | semidirect |
| 5. #26018222 | C2 | semidirect |
| 6. #26018210 | C2 | semidirect |
| 86. Q16×C89 | SD16 | semidirect |
| 167. C89 | #12379 | semidirect |
| 240. Q16 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022488 | 2 |
| #26022404 | 2 |
| #26019765 | 2 |
| #26018295 | 2 |
| #26018222 | 2 |
| #26018210 | 2 |
| C89×#3277 | 2 |
| #12379 | 89 |