Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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×#10622760 | C2 | semidirect |
| 3. #13070352 | C2 | semidirect |
| 4. #13070332 | C2 | semidirect |
| 5. #13069514 | C2 | semidirect |
| 6. #13066702 | C2 | semidirect |
| 7. C11×#3155 | C2 | semidirect |
| 61. C2×Dic44 | D4 | semidirect |
| 66. C2×D88 | D4 | semidirect |
| 82. #66876 | D4 | semidirect |
| 84. C2×C11⋊C16 | D4 | semidirect |
| 150. #3155 | 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×#10622760 | 2 |
| #13070352 | 2 |
| #13070332 | 2 |
| #13069514 | 2 |
| #13066702 | 2 |
| C11×#3155 | 2 |
| #13334 | 11 |