Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 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×#11745294 | C2 | semidirect |
| 2. C4×#90805 | C2 | semidirect |
| 3. #14271360 | C2 | semidirect |
| 4. #14271355 | C2 | semidirect |
| 5. #14271187 | C2 | semidirect |
| 6. #14271168 | C2 | semidirect |
| 7. C2×C29×#127 | C2 | semidirect |
| 15. C2×#90783 | C22 | semidirect |
| 17. C2×#90782 | C22 | semidirect |
| 21. C4×D116 | C22 | semidirect |
| 24. C4×Dic58 | C22 | semidirect |
| 25. #11745180 | C22 | semidirect |
| 26. C4⋊#6597 | C22 | semidirect |
| 39. #90805 | D4 | semidirect |
| 78. D116 | C2×D4 | semidirect |
| 82. Dic58 | C2×D4 | semidirect |
| 95. C4×C29 | AGL(1,ℤ/8) | semidirect |
| 101. C2×#127 | D29 | semidirect |
| 131. C29 | #3038 | semidirect |
| 200. C4 | #11745294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745294 | 2 |
| C4×#90805 | 2 |
| #14271360 | 2 |
| #14271355 | 2 |
| #14271187 | 2 |
| #14271168 | 2 |
| C2×C29×#127 | 2 |
| #3038 | 29 |