Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
338 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 18. C2×Q16×C29 | C4 | semidirect |
| 19. C2×#90785 | C4 | semidirect |
| 20. C2×#90785 | C4 | semidirect |
| 23. C2×Dic116 | C4 | semidirect |
| 81. C2×#1181 | Q16 | semidirect |
| 152. C2×Q16 | #1181 | semidirect |
| 166. C29 | #1878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#1181 | 2 |
| C2×#11745225 | 2 |
| (C2×#1181)⋊Q8 | 2 |
| #14272037 | 2 |
| (C2×#1181)⋊C8 | 2 |
| C2×Q16×D29 | 2 |
| #1878 | 29 |