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. #14271697 | C2 | semidirect |
| 2. C2×C4×D116 | C2 | semidirect |
| 3. #14271494 | C2 | semidirect |
| 4. #14271477 | C2 | semidirect |
| 5. #14271464 | C2 | semidirect |
| 6. #14271379 | C2 | semidirect |
| 7. #14271316 | C2 | semidirect |
| 9. #14271276 | C2 | semidirect |
| 10. #14271265 | C2 | semidirect |
| 11. C29×#432 | C2 | semidirect |
| 24. #11745237 | C22 | semidirect |
| 29. C4×D116 | C22 | semidirect |
| 31. #11745232 | C22 | semidirect |
| 32. C4×Dic58 | C22 | semidirect |
| 33. C29×C4⋊C8 | C22 | semidirect |
| 36. C29×#97 | C22 | semidirect |
| 39. #11745169 | C22 | semidirect |
| 40. #11745166 | C22 | semidirect |
| 41. #11745165 | C22 | semidirect |
| 42. #11745164 | C22 | semidirect |
| 145. #432 | D29 | semidirect |
| 175. C4⋊C8 | C2×D29 | semidirect |
| 182. #97 | 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 |
|---|---|
| #14271697 | 2 |
| C2×C4×D116 | 2 |
| #14271494 | 2 |
| #14271477 | 2 |
| #14271464 | 2 |
| #14271379 | 2 |
| #14271316 | 2 |
| #14271299 | 2 |
| #14271276 | 2 |
| #14271265 | 2 |
| C29×#432 | 2 |
| #3114 | 29 |