Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 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 |
|---|---|---|
| 2. C2×C4×Dic58 | C2 | semidirect |
| 3. #14271068 | C2 | semidirect |
| 5. #14271051 | C2 | semidirect |
| 6. #14271036 | C2 | semidirect |
| 7. #14271032 | C2 | semidirect |
| 8. #14271009 | C2 | semidirect |
| 19. #11745298 | C4 | semidirect |
| 46. C2×Dic58 | C2×C4 | semidirect |
| 51. C22⋊Dic29 | C2×C4 | semidirect |
| 57. C4×Dic29 | C2×C4 | semidirect |
| 141. C29 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745298 | 2 |
| C2×C4×Dic58 | 2 |
| #14271068 | 2 |
| #14271066 | 2 |
| #14271051 | 2 |
| #14271036 | 2 |
| #14271032 | 2 |
| #14271009 | 2 |
| C2×C4×D4×C29 | 2 |
| #2326 | 29 |