Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
310 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 310 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 |
|---|---|---|
| 39. C2×C11×C16 | Q8 | semidirect |
| 41. C11×#108 | Q8 | semidirect |
| 53. #66876 | Q8 | semidirect |
| 163. C2×C16 | Dic22 | semidirect |
| 168. #108 | Dic22 | semidirect |
| 214. C11 | #13460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079144 | 2 |
| #13070389 | 2 |
| C2×#10622125 | 2 |
| #13069407 | 2 |
| #13066730 | 2 |
| #13066701 | 2 |
| C11×#1383 | 2 |
| #13460 | 11 |