Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
316 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 2. #13070889 | C2 | semidirect |
| 3. #13068007 | C2 | semidirect |
| 4. #13066670 | C2 | semidirect |
| 5. #13066594 | C2 | semidirect |
| 63. C11×D8 | Q16 | semidirect |
| 189. D8 | #4326 | semidirect |
| 208. C11 | #12404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic22 | 2 |
| #13070889 | 2 |
| #13068007 | 2 |
| #13066670 | 2 |
| #13066594 | 2 |
| #13066577 | 2 |
| C11×#2224 | 2 |
| #12404 | 11 |