Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
618 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 618 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 |
|---|---|---|
| 1. C2×#11745185 | C2 | semidirect |
| 2. #14271127 | C2 | semidirect |
| 3. C4×C22⋊Dic29 | C2 | semidirect |
| 8. C2×#41×C29 | C4 | semidirect |
| 10. C22×Q8×C29 | C4 | semidirect |
| 12. C22×D4×C29 | C4 | semidirect |
| 16. C2×C4×Dic29 | C22 | semidirect |
| 17. C2×#90777 | C22 | semidirect |
| 67. Q8×C29 | C22⋊C4 | semidirect |
| 72. D4×C29 | C22⋊C4 | semidirect |
| 104. C22×C29 | #104 | semidirect |
| 127. C2×#41 | Dic29 | semidirect |
| 129. C22×Q8 | Dic29 | semidirect |
| 131. C22×D4 | Dic29 | semidirect |
| 141. C29 | #1789 | semidirect |
| 187. Q8 | C22⋊Dic29 | semidirect |
| 192. D4 | C22⋊Dic29 | semidirect |
| 223. C22 | #11745185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745185 | 2 |
| #14271127 | 2 |
| C4×C22⋊Dic29 | 2 |
| C22×#41×C29 | 2 |
| #1789 | 29 |