Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
232 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 11. #11745212 | C4 | semidirect |
| 12. #11745211 | C4 | semidirect |
| 13. #11745210 | C4 | semidirect |
| 14. #11745209 | C4 | semidirect |
| 17. C4×C8×C29 | C4 | semidirect |
| 18. C8×Dic29 | C4 | semidirect |
| 19. C8×Dic29 | C4 | semidirect |
| 20. C4×#6597 | C4 | semidirect |
| 99. C4×C8 | #1181 | semidirect |
| 100. C29 | #1772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D29⋊#108 | 2 |
| #14272173 | 2 |
| #14272126 | 2 |
| #14272034 | 2 |
| C4×C8×D29 | 2 |
| #1772 | 29 |