Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
396 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 4. C2×C8×Dic29 | C2 | semidirect |
| 5. C4⋊C4×Dic29 | C2 | semidirect |
| 6. #14270925 | C2 | semidirect |
| 7. C29×#340 | C2 | semidirect |
| 19. #11745255 | C4 | semidirect |
| 21. #11745169 | C4 | semidirect |
| 23. #11745157 | C4 | semidirect |
| 42. C2×C8×C29 | C2×C4 | semidirect |
| 46. C4⋊C4×C29 | C2×C4 | semidirect |
| 49. C4⋊Dic29 | C2×C4 | semidirect |
| 55. C2×#6597 | C2×C4 | semidirect |
| 88. D116 | C42 | semidirect |
| 115. Dic29 | #102 | semidirect |
| 122. #340 | D29 | semidirect |
| 147. C29 | C4×#102 | semidirect |
| 169. C2×C8 | C4×D29 | semidirect |
| 175. C4⋊C4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745255 | 2 |
| C2×#11745169 | 2 |
| C2×#11745157 | 2 |
| C2×C8×Dic29 | 2 |
| C4⋊C4×Dic29 | 2 |
| #14270925 | 2 |
| C29×#340 | 2 |
| C4×#102 | 29 |