Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
412 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 170 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. #14272188 | C2 | direct (N × H) |
| 2. C2×#11745220 | C2 | semidirect |
| 3. C2×C4⋊#6599 | C2 | semidirect |
| 6. C2×#11745218 | C2 | semidirect |
| 7. C2×C4×#6599 | C2 | semidirect |
| 22. #11745220 | C22 | semidirect |
| 25. #11745218 | C22 | semidirect |
| 26. C4⋊#6599 | C22 | semidirect |
| 27. C4×#6599 | C22 | semidirect |
| 106. C2×C29 | #433 | semidirect |
| 130. C29 | C2×#433 | semidirect |
| 201. C2 | #14272188 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272188 | 2 |
| C2×#11745220 | 2 |
| C2×C4⋊#6599 | 2 |
| C2×#11745219 | 2 |
| C2×#11745218 | 2 |
| C2×C4×#6599 | 2 |
| C2×#11745254 | 2 |
| C2×#433 | 29 |