Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
778 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 778 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. #14272155 | C2 | semidirect |
| 4. #14272154 | C2 | semidirect |
| 5. #14272153 | C2 | semidirect |
| 6. C2×#11745223 | C2 | semidirect |
| 8. C29×H(5,𝔽2) | C4 | semidirect |
| 10. #11745364 | C4 | semidirect |
| 11. #11745364 | C4 | semidirect |
| 16. #11745359 | C4 | semidirect |
| 23. #11745345 | C22 | semidirect |
| 24. C2×C4⋊#1181 | C22 | semidirect |
| 25. D29⋊M16 | C22 | semidirect |
| 26. C2×D29⋊C8 | C22 | semidirect |
| 27. #11745225 | C22 | semidirect |
| 28. #11745225 | C22 | semidirect |
| 29. #11745223 | C22 | semidirect |
| 30. #11745223 | C22 | semidirect |
| 31. #11745223 | C22 | semidirect |
| 36. #41×C29 | C2×C4 | semidirect |
| 38. C2×D4×C29 | C2×C4 | semidirect |
| 42. #90809 | C2×C4 | semidirect |
| 48. #90807 | C2×C4 | semidirect |
| 56. D4×D29 | C2×C4 | semidirect |
| 62. #90805 | C2×C4 | semidirect |
| 64. C2×D116 | C2×C4 | semidirect |
| 159. H(5,𝔽2) | #1181 | semidirect |
| 178. C29 | #2897 | semidirect |
| 193. #41 | C2×#1181 | semidirect |
| 210. C2×D4 | 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 |
| #14272155 | 2 |
| #14272154 | 2 |
| #14272153 | 2 |
| C2×#11745223 | 2 |
| H(5,𝔽2)×D29 | 2 |
| #2897 | 29 |