Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#11745277 | C2 | semidirect |
| 2. C2×#11745273 | C2 | semidirect |
| 3. #14271711 | C2 | semidirect |
| 4. #124×D29 | C2 | semidirect |
| 5. #14271558 | C2 | semidirect |
| 6. #14271557 | C2 | semidirect |
| 7. #14271550 | C2 | semidirect |
| 8. #14271546 | C2 | semidirect |
| 9. #14271544 | C2 | semidirect |
| 10. #14271115 | C2 | semidirect |
| 11. C29×#496 | C2 | semidirect |
| 15. C2×SD16×C29 | C22 | semidirect |
| 17. C29×#127 | C22 | semidirect |
| 20. C2×#90785 | C22 | semidirect |
| 23. #11745298 | C22 | semidirect |
| 26. C2×#90783 | C22 | semidirect |
| 30. C2×Dic116 | C22 | semidirect |
| 37. #11745231 | C22 | semidirect |
| 38. C29×#97 | C22 | semidirect |
| 39. C8×Dic29 | C22 | semidirect |
| 40. #11745151 | C22 | semidirect |
| 79. #90772 | D4 | semidirect |
| 136. #496 | D29 | semidirect |
| 156. C2×SD16 | C2×D29 | semidirect |
| 161. #127 | C2×D29 | semidirect |
| 173. #97 | C2×D29 | semidirect |
| 175. C29 | #3153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745277 | 2 |
| C2×#11745273 | 2 |
| #14271711 | 2 |
| #124×D29 | 2 |
| #14271558 | 2 |
| #14271557 | 2 |
| #14271550 | 2 |
| #14271546 | 2 |
| #14271544 | 2 |
| #14271115 | 2 |
| C29×#496 | 2 |
| #3153 | 29 |