Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#10622525 | C2 | semidirect |
| 2. #13079043 | C2 | semidirect |
| 3. #13070874 | C2 | semidirect |
| 4. #13070871 | C2 | semidirect |
| 5. #13070869 | C2 | semidirect |
| 6. C4×C16×D11 | C2 | semidirect |
| 7. C11×#2246 | C2 | semidirect |
| 51. C16×D11 | D4 | semidirect |
| 86. #2246 | D11 | semidirect |
| 131. C4×C11 | #508 | semidirect |
| 196. C11 | #33713 | semidirect |
| 226. C4 | #10622525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622525 | 2 |
| #13079043 | 2 |
| #13070874 | 2 |
| #13070871 | 2 |
| #13070869 | 2 |
| C4×C16×D11 | 2 |
| C11×#2246 | 2 |
| #33713 | 11 |