Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
676 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 143 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×#10622532 | C2 | semidirect |
| 2. #13080336 | C2 | semidirect |
| 3. #13070704 | C2 | semidirect |
| 4. #13070658 | C2 | semidirect |
| 5. #13070555 | C2 | semidirect |
| 6. C4×D176 | C2 | semidirect |
| 7. C16×D44 | C2 | semidirect |
| 8. C11×#2247 | C2 | semidirect |
| 56. D176 | D4 | semidirect |
| 93. #2247 | D11 | semidirect |
| 150. C4×C11 | #508 | semidirect |
| 221. C11 | #33849 | semidirect |
| 255. C4 | #10622532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622532 | 2 |
| #13080336 | 2 |
| #13070704 | 2 |
| #13070658 | 2 |
| #13070555 | 2 |
| C4×D176 | 2 |
| C16×D44 | 2 |
| C11×#2247 | 2 |
| #33849 | 11 |