Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
504 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 139 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. #13079127 | C2 | semidirect |
| 3. #13070896 | C2 | semidirect |
| 4. #13070841 | C2 | semidirect |
| 5. #13070840 | C2 | semidirect |
| 6. #13070810 | C2 | semidirect |
| 7. #13070776 | C2 | semidirect |
| 8. #13070413 | C2 | semidirect |
| 9. C11×#2252 | C2 | semidirect |
| 114. #2252 | D11 | semidirect |
| 270. C11 | #33794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079196 | 2 |
| #13079127 | 2 |
| #13070896 | 2 |
| #13070841 | 2 |
| #13070840 | 2 |
| #13070810 | 2 |
| #13070776 | 2 |
| #13070413 | 2 |
| C11×#2252 | 2 |
| #33794 | 11 |