Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745313 | C2 | semidirect |
| 2. C2×#11745311 | C2 | semidirect |
| 3. C2×#11745237 | C2 | semidirect |
| 4. #14271555 | C2 | semidirect |
| 5. #14271550 | C2 | semidirect |
| 6. #14271545 | C2 | semidirect |
| 7. C4×#90777 | C2 | semidirect |
| 8. C29×#532 | C2 | semidirect |
| 12. C29×C4⋊Q8 | C22 | semidirect |
| 13. C29×#127 | C22 | semidirect |
| 14. C29×#124 | C22 | semidirect |
| 20. C2×#90785 | C22 | semidirect |
| 22. C2×#90783 | C22 | semidirect |
| 29. #11745151 | C22 | semidirect |
| 30. C4×#6597 | C22 | semidirect |
| 59. #90777 | D4 | semidirect |
| 104. #532 | D29 | semidirect |
| 125. C4⋊Q8 | C2×D29 | semidirect |
| 126. #127 | C2×D29 | semidirect |
| 130. #124 | C2×D29 | semidirect |
| 137. C29 | #3153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745313 | 2 |
| C2×#11745311 | 2 |
| C2×#11745237 | 2 |
| #14271555 | 2 |
| #14271550 | 2 |
| #14271545 | 2 |
| C4×#90777 | 2 |
| C29×#532 | 2 |
| #3153 | 29 |