Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
586 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 99 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×#10622806 | C2 | semidirect |
| 2. C22×D176 | C2 | semidirect |
| 3. #13079103 | C2 | semidirect |
| 4. C2×#10622133 | C2 | semidirect |
| 5. #13069524 | C2 | semidirect |
| 6. #13066704 | C2 | semidirect |
| 7. C2×C11×#359 | C2 | semidirect |
| 64. C2×D88 | D4 | semidirect |
| 67. C2×C11×C16 | D4 | semidirect |
| 77. #66876 | D4 | semidirect |
| 143. C2×#359 | D11 | semidirect |
| 272. C2×C16 | C22⋊D11 | semidirect |
| 344. C11 | #13336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622806 | 2 |
| C22×D176 | 2 |
| #13079103 | 2 |
| C2×#10622133 | 2 |
| #13069524 | 2 |
| #13066704 | 2 |
| C2×C11×#359 | 2 |
| #13336 | 11 |