Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
168 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 59 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. #13066817 | C2 | semidirect |
| 3. #13066815 | C2 | semidirect |
| 4. #13066797 | C2 | semidirect |
| 5. #13066797 | C2 | semidirect |
| 137. C11 | #13716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070400 | 2 |
| #13066817 | 2 |
| #13066815 | 2 |
| #13066797 | 2 |
| C22⋊(C11⋊C32) | 2 |
| C11×#2216 | 2 |
| #13716 | 11 |