Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
464 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 87 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. #13070307 | C2 | semidirect |
| 3. #13070267 | C2 | semidirect |
| 4. #13070266 | C2 | semidirect |
| 5. #13068664 | C2 | semidirect |
| 6. #13068419 | C2 | semidirect |
| 7. C11×#2134 | C2 | semidirect |
| 11. C22×#4323 | C4 | semidirect |
| 16. #10622828 | C4 | semidirect |
| 23. #10622614 | C4 | semidirect |
| 24. #10622611 | C4 | semidirect |
| 146. #2134 | D11 | semidirect |
| 360. C11 | #13234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13078261 | 2 |
| #13070307 | 2 |
| #13070267 | 2 |
| #13070266 | 2 |
| #13068664 | 2 |
| #13068419 | 2 |
| C11×#2134 | 2 |
| #13234 | 11 |