Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
696 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 696 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×#10622525 | C2 | semidirect |
| 2. #13080374 | C2 | semidirect |
| 3. #13070699 | C2 | semidirect |
| 4. #13070653 | C2 | semidirect |
| 5. #13070536 | C2 | semidirect |
| 6. C4×Dic88 | C2 | semidirect |
| 7. C16×D44 | C2 | semidirect |
| 8. C11×#2246 | C2 | semidirect |
| 56. Dic88 | D4 | semidirect |
| 93. #2246 | D11 | semidirect |
| 151. C4×C11 | #508 | semidirect |
| 223. C11 | #33853 | semidirect |
| 259. 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 |
| #13080374 | 2 |
| #13070699 | 2 |
| #13070653 | 2 |
| #13070536 | 2 |
| C4×Dic88 | 2 |
| C16×D44 | 2 |
| C11×#2246 | 2 |
| #33853 | 11 |