Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
450 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26021025 | C2 | semidirect |
| 3. #26018925 | C2 | semidirect |
| 4. C2×#19151343 | C2 | semidirect |
| 6. #26018102 | C2 | semidirect |
| 192. C89 | #10550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030712 | 2 |
| #26021025 | 2 |
| #26018925 | 2 |
| C2×#19151343 | 2 |
| #26018651 | 2 |
| #26018102 | 2 |
| C89×#1547 | 2 |
| #10550 | 89 |