Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
738 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 198 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. #14272242 | C2 | semidirect |
| 2. #41×#1181 | C2 | semidirect |
| 3. #14272161 | C2 | semidirect |
| 4. #14272160 | C2 | semidirect |
| 5. D29⋊#104 | C2 | semidirect |
| 6. C2×#11745224 | C2 | semidirect |
| 8. C29×H(5,𝔽2) | C4 | semidirect |
| 10. #11745365 | C4 | semidirect |
| 11. #11745365 | C4 | semidirect |
| 16. #11745359 | C4 | semidirect |
| 23. #11745345 | C22 | semidirect |
| 24. C2×C4×#1181 | C22 | semidirect |
| 25. D29⋊M16 | C22 | semidirect |
| 26. C2×#90796 | C22 | semidirect |
| 27. #11745226 | C22 | semidirect |
| 28. #11745226 | C22 | semidirect |
| 29. #11745224 | C22 | semidirect |
| 30. #11745224 | C22 | semidirect |
| 31. #11745224 | C22 | semidirect |
| 35. #41×C29 | C2×C4 | semidirect |
| 37. C2×D4×C29 | C2×C4 | semidirect |
| 44. Q8×D29 | C2×C4 | semidirect |
| 52. #90807 | C2×C4 | semidirect |
| 57. D4×D29 | C2×C4 | semidirect |
| 62. #90805 | C2×C4 | semidirect |
| 66. C2×Dic58 | C2×C4 | semidirect |
| 152. H(5,𝔽2) | #1181 | semidirect |
| 171. C29 | #2901 | semidirect |
| 189. #41 | C2×#1181 | semidirect |
| 202. C2×D4 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272242 | 2 |
| #41×#1181 | 2 |
| #14272161 | 2 |
| #14272160 | 2 |
| D29⋊#104 | 2 |
| C2×#11745224 | 2 |
| #14271998 | 2 |
| #2901 | 29 |