Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 462 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 |
|---|---|---|
| 2. C2×#10622126 | C2 | semidirect |
| 3. #13070329 | C2 | semidirect |
| 4. #13070328 | C2 | semidirect |
| 5. #13069360 | C2 | semidirect |
| 6. #13066699 | C2 | semidirect |
| 7. C2×C11×#360 | C2 | semidirect |
| 69. C11×#106 | D4 | semidirect |
| 144. C2×#360 | D11 | semidirect |
| 280. #106 | C22⋊D11 | semidirect |
| 354. C11 | #13410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079059 | 2 |
| C2×#10622126 | 2 |
| #13070329 | 2 |
| #13070328 | 2 |
| #13069360 | 2 |
| #13066699 | 2 |
| C2×C11×#360 | 2 |
| #13410 | 11 |