Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 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. #13070658 | C2 | semidirect |
| 3. C8×D88 | C2 | semidirect |
| 4. #13066686 | C2 | semidirect |
| 5. #13066665 | C2 | semidirect |
| 6. #13066662 | C2 | semidirect |
| 7. C11×#1709 | C2 | semidirect |
| 77. #1709 | D11 | semidirect |
| 192. C11 | #12428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070658 | 2 |
| #13070648 | 2 |
| C8×D88 | 2 |
| #13066686 | 2 |
| #13066665 | 2 |
| #13066662 | 2 |
| C11×#1709 | 2 |
| #12428 | 11 |