Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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. #13070872 | C2 | semidirect |
| 2. #13070871 | C2 | semidirect |
| 3. #13070865 | C2 | semidirect |
| 4. #13068230 | C2 | semidirect |
| 5. #13068221 | C2 | semidirect |
| 6. #13066532 | C2 | semidirect |
| 7. C11×#2246 | C2 | semidirect |
| 65. C11×C16 | D8 | semidirect |
| 66. C11⋊C16 | D8 | semidirect |
| 70. #2246 | D11 | semidirect |
| 167. C16 | #4323 | semidirect |
| 168. C11 | #12519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070872 | 2 |
| #13070871 | 2 |
| #13070865 | 2 |
| #13068230 | 2 |
| #13068221 | 2 |
| #13066532 | 2 |
| C11×#2246 | 2 |
| #12519 | 11 |