Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
186 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 69 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. #13070497 | C2 | semidirect |
| 2. #13066820 | C2 | semidirect |
| 3. #13066800 | C2 | semidirect |
| 4. C32×Dic11 | C2 | semidirect |
| 8. C11×Q64 | C4 | semidirect |
| 9. C11×SD64 | C4 | semidirect |
| 10. C11×D32 | C4 | semidirect |
| 61. Q64 | Dic11 | semidirect |
| 62. SD64 | Dic11 | semidirect |
| 63. D32 | Dic11 | semidirect |
| 104. C11 | #13655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070497 | 2 |
| #13066820 | 2 |
| #13066800 | 2 |
| C32×Dic11 | 2 |
| C11×#2262 | 2 |
| #13655 | 11 |