Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2502 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2502 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. C22×#66929 | C2 | semidirect |
| 2. #13076690 | C2 | direct (N × H) |
| 3. C2×#10622596 | C2 | semidirect |
| 4. C2×#10622607 | C2 | semidirect |
| 6. C2×C11×#384 | C2 | semidirect |
| 16. C2×#66929 | C22 | semidirect |
| 17. C11×#384 | C22 | semidirect |
| 20. #10622607 | C22 | semidirect |
| 22. #10622596 | C22 | semidirect |
| 34. C2×C42×C11 | D4 | semidirect |
| 70. C42×C11 | C2×D4 | semidirect |
| 80. C2×#384 | D11 | semidirect |
| 118. #384 | C2×D11 | semidirect |
| 155. C2×C42 | D44 | semidirect |
| 159. C2×C11 | #2823 | semidirect |
| 190. C42 | C2×D44 | semidirect |
| 191. C11 | C2×#2823 | semidirect |
| 231. C2 | #13076690 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66929 | 2 |
| #13076690 | 2 |
| C2×#10622596 | 2 |
| C2×#10622607 | 2 |
| C2×#10622604 | 2 |
| C2×C11×#384 | 2 |
| C2×#2823 | 11 |