Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
560 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 160 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. (C2×#1181)⋊Q8 | C2 | semidirect |
| 2. #14272113 | C2 | semidirect |
| 4. C22⋊C4×#1181 | C2 | semidirect |
| 5. #14272099 | C2 | semidirect |
| 15. C29×#124 | C4 | semidirect |
| 16. #11745309 | C4 | semidirect |
| 17. #11745298 | C4 | semidirect |
| 18. #11745247 | C4 | semidirect |
| 20. #11745237 | C4 | semidirect |
| 31. C2×Q8×C29 | C2×C4 | semidirect |
| 42. C2×Dic58 | C2×C4 | semidirect |
| 43. C2×Dic58 | C2×C4 | semidirect |
| 49. C22⋊C4×C29 | C2×C4 | semidirect |
| 50. C42×C29 | C2×C4 | semidirect |
| 51. C22⋊Dic29 | C2×C4 | semidirect |
| 52. #90781 | C2×C4 | semidirect |
| 53. #90781 | C2×C4 | semidirect |
| 54. C4×Dic29 | C2×C4 | semidirect |
| 55. C4×Dic29 | C2×C4 | semidirect |
| 126. #124 | #1181 | semidirect |
| 138. C29 | #2372 | semidirect |
| 144. C2×Q8 | C2×#1181 | semidirect |
| 163. C22⋊C4 | C2×#1181 | semidirect |
| 168. C42 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#1181)⋊Q8 | 2 |
| #14272113 | 2 |
| #14272111 | 2 |
| C22⋊C4×#1181 | 2 |
| #14272099 | 2 |
| #124×D29 | 2 |
| #2372 | 29 |