Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
298 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 67 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. #13070863 | C2 | semidirect |
| 2. #13070661 | C2 | semidirect |
| 3. #13068105 | C2 | semidirect |
| 4. #13066668 | C2 | semidirect |
| 5. #13066583 | C2 | semidirect |
| 6. #13066574 | C2 | semidirect |
| 243. C11 | #12350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070863 | 2 |
| #13070661 | 2 |
| #13068105 | 2 |
| #13066668 | 2 |
| #13066583 | 2 |
| #13066574 | 2 |
| C11×#3355 | 2 |
| #12350 | 11 |