Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 12. C29×#97 | C4 | semidirect |
| 13. #11745163 | C4 | semidirect |
| 14. C8×Dic29 | C4 | semidirect |
| 15. #11745151 | C4 | semidirect |
| 42. C8×C29 | C42 | semidirect |
| 43. #6597 | C42 | semidirect |
| 53. Dic29 | #97 | direct (N × H) |
| 71. #97 | Dic29 | direct (N × H) |
| 73. C29 | C4×#97 | semidirect |
| 101. C8 | C4×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745151 | 2 |
| C2×#11745163 | 2 |
| C2×C8×Dic29 | 2 |
| C42×Dic29 | 2 |
| C2×C29×#97 | 2 |
| C4×#97 | 29 |