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×#11745280 | C2 | semidirect |
| 2. C2×#11745276 | C2 | semidirect |
| 3. #14271714 | C2 | semidirect |
| 4. #124×D29 | C2 | semidirect |
| 5. #14271555 | C2 | semidirect |
| 6. #14271553 | C2 | semidirect |
| 7. #14271552 | C2 | semidirect |
| 8. #14271548 | C2 | semidirect |
| 9. #14271544 | C2 | semidirect |
| 10. #14271115 | C2 | semidirect |
| 11. C29×#497 | C2 | semidirect |
| 15. C2×Q16×C29 | C22 | semidirect |
| 17. C29×C4⋊Q8 | C22 | semidirect |
| 20. #11745309 | C22 | semidirect |
| 21. C2×#90785 | C22 | semidirect |
| 23. C2×#90784 | C22 | semidirect |
| 29. C2×#90773 | C22 | semidirect |
| 36. #11745236 | C22 | semidirect |
| 38. C29×#97 | C22 | semidirect |
| 39. C8×Dic29 | C22 | semidirect |
| 40. #11745151 | C22 | semidirect |
| 79. #90772 | D4 | semidirect |
| 134. #497 | D29 | semidirect |
| 152. C2×Q16 | C2×D29 | semidirect |
| 160. C4⋊Q8 | 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×#11745280 | 2 |
| C2×#11745276 | 2 |
| #14271714 | 2 |
| #124×D29 | 2 |
| #14271555 | 2 |
| #14271553 | 2 |
| #14271552 | 2 |
| #14271548 | 2 |
| #14271544 | 2 |
| #14271115 | 2 |
| C29×#497 | 2 |
| #3153 | 29 |