Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
464 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 160 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. #14272197 | C2 | semidirect |
| 2. #14272193 | C2 | semidirect |
| 3. #14272191 | C2 | semidirect |
| 4. #14272184 | C2 | semidirect |
| 5. #14272180 | C2 | semidirect |
| 6. #14272134 | C2 | semidirect |
| 7. D29⋊(C22⋊C8) | C2 | semidirect |
| 11. C2×#90796 | C22 | semidirect |
| 12. C2×D29⋊C8 | C22 | semidirect |
| 25. #11745220 | C22 | semidirect |
| 26. #11745219 | C22 | semidirect |
| 27. #11745219 | C22 | semidirect |
| 28. #11745218 | C22 | semidirect |
| 29. C4⋊#6599 | C22 | semidirect |
| 30. C4×#6599 | C22 | semidirect |
| 81. D116 | M16 | semidirect |
| 145. C29 | #2974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272197 | 2 |
| #14272193 | 2 |
| #14272191 | 2 |
| #14272184 | 2 |
| #14272180 | 2 |
| #14272134 | 2 |
| D29⋊(C22⋊C8) | 2 |
| C2×#11745255 | 2 |
| #2974 | 29 |