Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
732 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 243 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 |
|---|---|---|
| 3. #13069171 | C2 | semidirect |
| 4. #13068487 | C2 | semidirect |
| 6. C42×C11⋊C8 | C2 | semidirect |
| 7. C11×#1839 | C2 | semidirect |
| 66. C42×C11 | M16 | semidirect |
| 81. #1839 | D11 | semidirect |
| 109. C11⋊C8 | #126 | semidirect |
| 195. C42 | #4313 | semidirect |
| 196. C11 | #21666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#66929 | 2 |
| #13069220 | 2 |
| #13069171 | 2 |
| #13068487 | 2 |
| #13068396 | 2 |
| C42×C11⋊C8 | 2 |
| C11×#1839 | 2 |
| #21666 | 11 |