Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
4830 conjugacy classes of subgroups; only the 763 normal subgroups are shown.
This group has 4830 conjugacy classes of subgroups — too many to draw. Only its 763 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. #13066887 | C2 | semidirect |
| 4. #13066886 | C2 | semidirect |
| 5. C11×#1446 | C2 | semidirect |
| 8. C22×Q8×D11 | C4 | semidirect |
| 18. C22×Q8×C11 | C2×C4 | semidirect |
| 30. C22×C4×D11 | Q8 | semidirect |
| 33. C22×Dic22 | C2×C4 | semidirect |
| 50. C22×C4×C11 | C2×Q8 | semidirect |
| 56. C22×Dic11 | C2×Q8 | semidirect |
| 71. #1446 | D11 | direct (N × H) |
| 129. C22×Q8 | C4×D11 | semidirect |
| 147. D11 | #1446 | direct (N × H) |
| 176. C22×C4 | Q8×D11 | semidirect |
| 177. C11 | C2×#1446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×D11 | 2 |
| C2×D11×#95 | 2 |
| #13066887 | 2 |
| #13066886 | 2 |
| C11×#1446 | 2 |
| C2×#1446 | 11 |