Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
380 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 2. #14272105 | C2 | semidirect |
| 3. #14272041 | C2 | semidirect |
| 5. C23×C4×C29 | C4 | semidirect |
| 10. C2×C22⋊Dic29 | C4 | semidirect |
| 14. C2×#90779 | C4 | semidirect |
| 15. C2×C4×Dic29 | C4 | semidirect |
| 48. C23×C29 | C4⋊C4 | semidirect |
| 74. C2×Dic29 | C4⋊C4 | semidirect |
| 98. C4×C29 | #99 | semidirect |
| 116. C23×C4 | #1181 | semidirect |
| 127. C29 | #1799 | semidirect |
| 164. C23 | C4⋊#1181 | semidirect |
| 210. C4 | #11745227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745227 | 2 |
| #14272105 | 2 |
| #14272041 | 2 |
| C2×C4×C22⋊D29 | 2 |
| #1799 | 29 |