Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #14271529 | C2 | semidirect |
| 3. #14271511 | C2 | semidirect |
| 4. #14271167 | C2 | semidirect |
| 5. C4×#90777 | C2 | semidirect |
| 6. C29×#533 | C2 | semidirect |
| 9. C29×C4⋊Q8 | C22 | semidirect |
| 10. C29×#125 | C22 | semidirect |
| 19. #11745157 | C22 | semidirect |
| 20. #11745151 | C22 | semidirect |
| 21. C4×#6597 | C22 | semidirect |
| 71. #533 | D29 | semidirect |
| 84. C4⋊Q8 | C2×D29 | semidirect |
| 88. #125 | C2×D29 | semidirect |
| 96. C29 | #3138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745236 | 2 |
| #14271529 | 2 |
| #14271511 | 2 |
| #14271167 | 2 |
| C4×#90777 | 2 |
| C29×#533 | 2 |
| #3138 | 29 |