Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
494 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 109 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. #13077493 | C2 | semidirect |
| 3. C2×#10622148 | C2 | semidirect |
| 4. C2×#10622147 | C2 | semidirect |
| 5. #13069526 | C2 | semidirect |
| 6. #13066725 | C2 | semidirect |
| 7. C11×#1379 | C2 | semidirect |
| 20. #10622521 | C4 | semidirect |
| 45. C2×D88 | C2×C4 | semidirect |
| 54. C11×M32 | C2×C4 | semidirect |
| 130. #1379 | D11 | semidirect |
| 237. M32 | C4×D11 | semidirect |
| 311. C11 | #13022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622521 | 2 |
| #13077493 | 2 |
| C2×#10622148 | 2 |
| C2×#10622147 | 2 |
| #13069526 | 2 |
| #13066725 | 2 |
| C11×#1379 | 2 |
| #13022 | 11 |