Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
558 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 558 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 |
|---|---|---|
| 2. #13070898 | C2 | semidirect |
| 3. #13070897 | C2 | semidirect |
| 4. #13070896 | C2 | semidirect |
| 7. C11×#2254 | C2 | semidirect |
| 47. C16×D11 | Q8 | semidirect |
| 71. C11×C16 | C2×Q8 | semidirect |
| 72. C11⋊C16 | C2×Q8 | semidirect |
| 77. #2254 | D11 | direct (N × H) |
| 150. D11 | #2254 | direct (N × H) |
| 174. C16 | Q8×D11 | semidirect |
| 175. C11 | C2×#2254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D11×#500 | 2 |
| #13070898 | 2 |
| #13070897 | 2 |
| #13070896 | 2 |
| D11×#367 | 2 |
| C4×C16×D11 | 2 |
| C11×#2254 | 2 |
| C2×#2254 | 11 |