Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
906 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 211 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. #13079191 | C2 | semidirect |
| 2. #13079044 | C2 | semidirect |
| 3. #13068288 | C2 | semidirect |
| 4. #13068285 | C2 | semidirect |
| 5. #13068283 | C2 | semidirect |
| 6. #13068280 | C2 | semidirect |
| 7. C2×#10622093 | C2 | semidirect |
| 8. C11×#3147 | C2 | semidirect |
| 81. C2×C8×C11 | D8 | semidirect |
| 99. #3147 | D11 | semidirect |
| 224. C2×C8 | #4323 | semidirect |
| 234. C11 | #19616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079191 | 2 |
| #13079044 | 2 |
| #13068288 | 2 |
| #13068285 | 2 |
| #13068283 | 2 |
| #13068280 | 2 |
| C2×#10622093 | 2 |
| C11×#3147 | 2 |
| #19616 | 11 |