Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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. #13081750 | C2 | semidirect |
| 2. C2×#10622521 | C2 | semidirect |
| 3. #13079103 | C2 | semidirect |
| 4. #13070331 | C2 | semidirect |
| 5. #13069512 | C2 | semidirect |
| 6. #13066703 | C2 | semidirect |
| 7. C11×#2145 | C2 | semidirect |
| 55. C2×Dic44 | D4 | semidirect |
| 66. C2×D88 | D4 | semidirect |
| 69. C11×M32 | D4 | semidirect |
| 81. C2×C11⋊C16 | D4 | semidirect |
| 151. #2145 | D11 | semidirect |
| 287. M32 | C22⋊D11 | semidirect |
| 364. C11 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081750 | 2 |
| C2×#10622521 | 2 |
| #13079103 | 2 |
| #13070331 | 2 |
| #13069512 | 2 |
| #13066703 | 2 |
| C11×#2145 | 2 |
| #13334 | 11 |