Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
396 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 3. C2×C4×#6597 | C2 | semidirect |
| 4. #14270925 | C2 | semidirect |
| 5. C4×C4⋊C4×C29 | C2 | semidirect |
| 15. C4×D116 | C4 | semidirect |
| 17. #11745157 | C4 | direct (N × H) |
| 33. C4⋊C4×C29 | C2×C4 | semidirect |
| 42. C2×#6597 | C2×C4 | semidirect |
| 66. D116 | C42 | semidirect |
| 82. C4×C29 | #102 | semidirect |
| 90. C4×C4⋊C4 | D29 | semidirect |
| 111. C29 | C4×#102 | semidirect |
| 131. C4⋊C4 | C4×D29 | semidirect |
| 175. C4 | #11745157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D116 | 2 |
| C2×#11745157 | 2 |
| C2×C4×#6597 | 2 |
| #14270925 | 2 |
| C4×C4⋊C4×C29 | 2 |
| C4×#102 | 29 |