Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
402 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 107 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×#10622128 | C2 | semidirect |
| 5. #13069402 | C2 | semidirect |
| 6. #13066706 | C2 | semidirect |
| 7. C11×#1387 | C2 | semidirect |
| 24. #10622135 | C4 | semidirect |
| 49. C11×#108 | C2×C4 | semidirect |
| 60. C2×C11⋊C16 | C2×C4 | semidirect |
| 112. #1387 | D11 | semidirect |
| 205. #108 | C4×D11 | semidirect |
| 265. C11 | #12946 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13077490 | 2 |
| C2×#10622128 | 2 |
| C2×#10622135 | 2 |
| #13070329 | 2 |
| #13069402 | 2 |
| #13066706 | 2 |
| C11×#1387 | 2 |
| #12946 | 11 |