Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×D116 | C2 | semidirect |
| 2. #14271491 | C2 | semidirect |
| 3. #14271474 | C2 | semidirect |
| 4. #14271460 | C2 | semidirect |
| 5. #14271375 | C2 | semidirect |
| 6. #14271313 | C2 | semidirect |
| 8. #14271273 | C2 | semidirect |
| 9. #14271261 | C2 | semidirect |
| 10. #14271220 | C2 | semidirect |
| 11. C29×#529 | C2 | semidirect |
| 15. C29×#125 | C22 | semidirect |
| 16. C29×#124 | C22 | semidirect |
| 20. C4×Q8×C29 | C22 | semidirect |
| 22. C4×D4×C29 | C22 | semidirect |
| 33. #11745183 | C22 | semidirect |
| 34. #11745180 | C22 | semidirect |
| 39. #11745156 | C22 | semidirect |
| 40. #11745155 | C22 | semidirect |
| 41. C4⋊#6597 | C22 | semidirect |
| 42. #11745151 | C22 | semidirect |
| 135. #529 | D29 | semidirect |
| 157. #125 | C2×D29 | semidirect |
| 158. #124 | C2×D29 | semidirect |
| 162. C4×Q8 | C2×D29 | semidirect |
| 168. C4×D4 | C2×D29 | semidirect |
| 183. C29 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D116 | 2 |
| #14271491 | 2 |
| #14271474 | 2 |
| #14271460 | 2 |
| #14271375 | 2 |
| #14271313 | 2 |
| #14271296 | 2 |
| #14271273 | 2 |
| #14271261 | 2 |
| #14271220 | 2 |
| C29×#529 | 2 |
| #3114 | 29 |