Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
464 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 168 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. #14272198 | C2 | semidirect |
| 2. #14272194 | C2 | semidirect |
| 3. D4×#6599 | C2 | semidirect |
| 4. #14272184 | C2 | semidirect |
| 5. #14272180 | C2 | semidirect |
| 6. #14272133 | C2 | semidirect |
| 7. C2×C22⋊#6599 | C2 | semidirect |
| 11. C2×#90800 | C22 | semidirect |
| 12. C22×#6599 | C22 | semidirect |
| 25. C22⋊#6599 | C22 | semidirect |
| 26. C22⋊#6599 | C22 | semidirect |
| 27. #11745220 | C22 | semidirect |
| 28. #11745218 | C22 | semidirect |
| 29. C4⋊#6599 | C22 | semidirect |
| 30. C4×#6599 | C22 | semidirect |
| 69. D4×C29 | M16 | semidirect |
| 145. C29 | #2974 | semidirect |
| 184. D4 | #90800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272198 | 2 |
| #14272194 | 2 |
| D4×#6599 | 2 |
| #14272184 | 2 |
| #14272180 | 2 |
| #14272133 | 2 |
| C2×C22⋊#6599 | 2 |
| C2×D4×Dic29 | 2 |
| #2974 | 29 |