Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11745276 | C2 | semidirect |
| 2. #14271714 | C2 | semidirect |
| 3. #127×D29 | C2 | semidirect |
| 4. #14271549 | C2 | semidirect |
| 5. #14271540 | C2 | semidirect |
| 6. #14271539 | C2 | semidirect |
| 7. #14271537 | C2 | semidirect |
| 8. C4×#90772 | C2 | semidirect |
| 9. C29×#492 | C2 | semidirect |
| 13. C2×SD16×C29 | C22 | semidirect |
| 14. C29×C4⋊Q8 | C22 | semidirect |
| 16. #11745309 | C22 | semidirect |
| 17. C2×#90784 | C22 | semidirect |
| 20. C2×#90782 | C22 | semidirect |
| 22. C2×D232 | C22 | semidirect |
| 27. #11745236 | C22 | semidirect |
| 29. C4×C8×C29 | C22 | semidirect |
| 30. #11745163 | C22 | semidirect |
| 31. C4×#6597 | C22 | semidirect |
| 60. #90772 | D4 | semidirect |
| 85. C8×C29 | C2×D4 | semidirect |
| 86. #6597 | C2×D4 | semidirect |
| 99. C4×C29 | AGL(1,ℤ/8) | semidirect |
| 110. #492 | D29 | semidirect |
| 123. C2×SD16 | C2×D29 | semidirect |
| 127. C4⋊Q8 | C2×D29 | semidirect |
| 139. C4×C8 | C2×D29 | semidirect |
| 140. C29 | #3151 | semidirect |
| 195. C8 | D4×D29 | semidirect |
| 209. C4 | #11745276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745276 | 2 |
| #14271714 | 2 |
| #127×D29 | 2 |
| #14271549 | 2 |
| #14271540 | 2 |
| #14271539 | 2 |
| #14271537 | 2 |
| C4×#90772 | 2 |
| C29×#492 | 2 |
| #3151 | 29 |