Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
562 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 167 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. #13081591 | C2 | semidirect |
| 2. #13070841 | C2 | semidirect |
| 3. #13070750 | C2 | semidirect |
| 4. #13070651 | C2 | semidirect |
| 5. Q8×C11⋊C16 | C2 | semidirect |
| 6. C4×#66890 | C2 | semidirect |
| 7. Q8×C11×D8 | C2 | semidirect |
| 58. C11×D8 | #41 | semidirect |
| 74. Q8×D8 | D11 | semidirect |
| 83. Q8×C11 | D16 | semidirect |
| 170. D8 | #4343 | semidirect |
| 182. C11 | #33925 | semidirect |
| 186. Q8 | #66890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081591 | 2 |
| #13070841 | 2 |
| #13070750 | 2 |
| #13070651 | 2 |
| Q8×C11⋊C16 | 2 |
| C4×#66890 | 2 |
| Q8×C11×D8 | 2 |
| #33925 | 11 |