Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
314 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 314 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. #13081008 | C2 | semidirect |
| 2. #13070653 | C2 | semidirect |
| 4. #13066674 | C2 | semidirect |
| 5. #13066581 | C2 | semidirect |
| 6. #13066572 | C2 | semidirect |
| 7. C11×#2240 | C2 | semidirect |
| 88. #2240 | D11 | semidirect |
| 110. D44 | SD32 | semidirect |
| 220. C11 | #12342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081008 | 2 |
| #13070653 | 2 |
| #13067968 | 2 |
| #13066674 | 2 |
| #13066581 | 2 |
| #13066572 | 2 |
| C11×#2240 | 2 |
| #12342 | 11 |