Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 178 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 |
|---|---|---|
| 10. C4×#6599 | C4 | semidirect |
| 11. #11745208 | C4 | direct (N × H) |
| 12. C4×C8×C29 | C4 | semidirect |
| 13. C8×Dic29 | C4 | semidirect |
| 14. C4×#6597 | C4 | semidirect |
| 37. #6599 | C42 | semidirect |
| 38. C8×C29 | C42 | semidirect |
| 39. #6597 | C42 | semidirect |
| 45. C4×C29 | #97 | semidirect |
| 47. Dic29 | #97 | semidirect |
| 65. C4×C8 | #1181 | semidirect |
| 66. C29 | C4×#97 | semidirect |
| 91. C8 | C4×#1181 | semidirect |
| 98. C4 | #11745208 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745208 | 2 |
| C4×D29⋊C8 | 2 |
| C42×#1181 | 2 |
| C4×C8×D29 | 2 |
| C4×#97 | 29 |