Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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. #13079103 | C2 | semidirect |
| 3. #13070352 | C2 | semidirect |
| 4. #13070333 | C2 | semidirect |
| 5. #13069515 | C2 | semidirect |
| 6. #13066701 | C2 | semidirect |
| 7. C11×#3414 | C2 | semidirect |
| 45. C2×C11×Q16 | D4 | semidirect |
| 49. C2×C11×D8 | D4 | semidirect |
| 74. C2×C11×C16 | D4 | semidirect |
| 84. #66876 | D4 | semidirect |
| 148. #3414 | D11 | semidirect |
| 257. C2×Q16 | C22⋊D11 | semidirect |
| 269. C2×D8 | C22⋊D11 | semidirect |
| 289. C2×C16 | 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 |
|---|---|
| C2×#10622806 | 2 |
| #13079103 | 2 |
| #13070352 | 2 |
| #13070333 | 2 |
| #13069515 | 2 |
| #13066701 | 2 |
| C11×#3414 | 2 |
| #13334 | 11 |