Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
680 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 338 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. #14272122 | C2 | direct (N × H) |
| 3. C2×#11745218 | C2 | semidirect |
| 8. C2×D29⋊C8 | C4 | semidirect |
| 15. #11745218 | C22 | semidirect |
| 26. C2×#6599 | C2×C4 | semidirect |
| 28. D29⋊C8 | C2×C4 | semidirect |
| 49. #6599 | C22×C4 | semidirect |
| 54. C2×D29 | #97 | semidirect |
| 66. C2×C29 | C2×#97 | semidirect |
| 69. D29 | C2×#97 | semidirect |
| 81. C29 | C22×#97 | semidirect |
| 128. C2 | #14272122 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D29⋊C8 | 2 |
| #14272122 | 2 |
| C2×#11745218 | 2 |
| C2×C42×D29 | 2 |
| C22×#97 | 29 |