Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
354 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 93 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. #13070404 | C2 | semidirect |
| 2. C2×#10622149 | C2 | semidirect |
| 5. #13069362 | C2 | semidirect |
| 6. #13066726 | C2 | semidirect |
| 239. C11 | #13478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070404 | 2 |
| C2×#10622149 | 2 |
| #13070332 | 2 |
| #13069483 | 2 |
| #13069362 | 2 |
| #13066726 | 2 |
| C2×C11×#361 | 2 |
| #13478 | 11 |