Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
442 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 76 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×C4×#1181 | C2 | semidirect |
| 2. C2×#11745226 | C2 | semidirect |
| 3. #14272134 | C2 | semidirect |
| 4. #14272033 | C2 | semidirect |
| 13. C29×C22⋊Q8 | C4 | semidirect |
| 14. #11745308 | C4 | semidirect |
| 15. #11745292 | C4 | semidirect |
| 16. #11745257 | C4 | semidirect |
| 30. C2×Q8×C29 | C2×C4 | semidirect |
| 38. C2×D116 | C2×C4 | semidirect |
| 49. C4×#1181 | D4 | semidirect |
| 53. C4⋊C4×C29 | C2×C4 | semidirect |
| 59. C4⋊Dic29 | C2×C4 | semidirect |
| 100. C22×C29 | #104 | semidirect |
| 111. C2×D29 | #104 | semidirect |
| 141. C22⋊Q8 | #1181 | semidirect |
| 154. C29 | #1896 | semidirect |
| 158. C2×Q8 | C2×#1181 | semidirect |
| 182. C4⋊C4 | C2×#1181 | semidirect |
| 241. C22 | #11745226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#1181 | 2 |
| C2×#11745226 | 2 |
| #14272134 | 2 |
| #14272033 | 2 |
| #14271676 | 2 |
| #1896 | 29 |