Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
688 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 152 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. #14272115 | C2 | semidirect |
| 2. #14272113 | C2 | semidirect |
| 3. #14272111 | C2 | semidirect |
| 4. #14272104 | C2 | semidirect |
| 7. C23×#1181 | C22 | semidirect |
| 11. C2×C22⋊#1181 | C22 | semidirect |
| 12. C2×C4⋊#1181 | C22 | semidirect |
| 13. C2×C4×#1181 | C22 | semidirect |
| 14. C29×#120 | C4 | semidirect |
| 15. #11745315 | C4 | semidirect |
| 16. #11745299 | C4 | semidirect |
| 17. #11745244 | C4 | semidirect |
| 19. (C2×#1181)⋊C4 | C22 | semidirect |
| 20. C24×C29 | C2×C4 | semidirect |
| 23. C23×D29 | C2×C4 | semidirect |
| 41. C22⋊C4×C29 | C2×C4 | semidirect |
| 42. C22⋊Dic29 | C2×C4 | semidirect |
| 43. #90781 | C2×C4 | semidirect |
| 112. #120 | #1181 | semidirect |
| 120. C29 | #2375 | semidirect |
| 126. C24 | C2×#1181 | semidirect |
| 143. C22⋊C4 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272115 | 2 |
| #14272113 | 2 |
| #14272111 | 2 |
| #14272104 | 2 |
| #120×D29 | 2 |
| #2375 | 29 |