Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
488 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 205 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. #14271257 | C2 | direct (N × H) |
| 14. C2×Dic116 | C4 | semidirect |
| 40. Dic116 | C2×C4 | semidirect |
| 51. C2×Dic29 | Q16 | semidirect |
| 70. Dic29 | C2×Q16 | semidirect |
| 77. C2×C29 | C4×Q16 | semidirect |
| 95. C29 | C2×C4×Q16 | semidirect |
| 145. C2 | #14271257 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic116 | 2 |
| C2×#11745249 | 2 |
| #14271257 | 2 |
| C2×#11745158 | 2 |
| C2×C8×Dic29 | 2 |
| C2×C29×#107 | 2 |
| C2×C4×Q16 | 29 |