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. #13081752 | C2 | semidirect |
| 2. C2×#10622521 | C2 | semidirect |
| 3. #13079102 | C2 | semidirect |
| 4. #13070353 | C2 | semidirect |
| 5. #13070333 | C2 | semidirect |
| 6. #13069514 | C2 | semidirect |
| 7. C11×#1378 | C2 | semidirect |
| 43. C2×Dic44 | D4 | semidirect |
| 60. C2×D88 | D4 | semidirect |
| 71. C11×M32 | D4 | semidirect |
| 73. C2×C11×C16 | D4 | semidirect |
| 154. #1378 | D11 | semidirect |
| 287. M32 | D44 | semidirect |
| 289. C2×C16 | D44 | semidirect |
| 364. C11 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081752 | 2 |
| C2×#10622521 | 2 |
| #13079102 | 2 |
| #13070353 | 2 |
| #13070333 | 2 |
| #13069514 | 2 |
| C11×#1378 | 2 |
| #13334 | 11 |