Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2130 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2130 conjugacy classes of subgroups — too many to draw. Only its 667 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. #13076998 | C2 | semidirect |
| 2. #13076983 | C2 | semidirect |
| 3. #13076931 | C2 | semidirect |
| 4. C4×#66929 | C2 | semidirect |
| 6. #13071099 | C2 | semidirect |
| 7. C2×C43×C11 | C2 | semidirect |
| 66. C42×C11 | #41 | semidirect |
| 78. C2×C43 | D11 | semidirect |
| 87. C2×C4×C11 | #126 | semidirect |
| 175. C42 | #4339 | semidirect |
| 176. C11 | #36641 | semidirect |
| 192. C2×C4 | #66929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13076998 | 2 |
| #13076983 | 2 |
| #13076931 | 2 |
| C4×#66929 | 2 |
| #13071106 | 2 |
| #13071099 | 2 |
| C2×C43×C11 | 2 |
| #36641 | 11 |