Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
814 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 199 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 |
|---|---|---|
| 3. #13070869 | C2 | semidirect |
| 4. #13070868 | C2 | semidirect |
| 5. #13070867 | C2 | semidirect |
| 7. C11×#2247 | C2 | semidirect |
| 86. #2247 | D11 | direct (N × H) |
| 98. C4×D11 | Q32 | semidirect |
| 129. C4×C11 | C2×Q32 | semidirect |
| 134. Dic11 | C2×Q32 | semidirect |
| 164. D11 | #2247 | direct (N × H) |
| 193. C11 | C2×#2247 | semidirect |
| 221. C4 | D11×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D11×Q32 | 2 |
| D11×#494 | 2 |
| #13070869 | 2 |
| #13070868 | 2 |
| #13070867 | 2 |
| C4×C16×D11 | 2 |
| C11×#2247 | 2 |
| C2×#2247 | 11 |