Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
726 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 200 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. D29⋊#131 | C2 | semidirect |
| 2. #14272232 | C2 | semidirect |
| 3. #14272156 | C2 | semidirect |
| 4. #14272154 | C2 | semidirect |
| 5. #14272153 | C2 | semidirect |
| 6. C2×#11745225 | C2 | semidirect |
| 8. C29×2−1+4 | C4 | semidirect |
| 10. #11745365 | C4 | semidirect |
| 11. #11745365 | C4 | semidirect |
| 16. #11745362 | C4 | semidirect |
| 35. #41×C29 | C2×C4 | semidirect |
| 37. C2×Q8×C29 | C2×C4 | semidirect |
| 39. #90809 | C2×C4 | semidirect |
| 45. Q8×D29 | C2×C4 | semidirect |
| 51. #90807 | C2×C4 | semidirect |
| 60. #90805 | C2×C4 | semidirect |
| 66. C2×Dic58 | C2×C4 | semidirect |
| 154. 2−1+4 | #1181 | semidirect |
| 173. C29 | #2898 | semidirect |
| 189. #41 | C2×#1181 | semidirect |
| 201. C2×Q8 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D29⋊#131 | 2 |
| #14272232 | 2 |
| #14272156 | 2 |
| #14272154 | 2 |
| #14272153 | 2 |
| C2×#11745225 | 2 |
| 2−1+4×D29 | 2 |
| #2898 | 29 |