Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#11745266 | C2 | semidirect |
| 2. #14271595 | C2 | direct (N × H) |
| 3. C2×Dic232 | C2 | semidirect |
| 4. C2×#11745148 | C2 | semidirect |
| 5. C2×D464 | C2 | semidirect |
| 6. C22×C16×C29 | C2 | semidirect |
| 11. #11745266 | C22 | semidirect |
| 16. C2×C16×C29 | C22 | semidirect |
| 17. Dic232 | C22 | semidirect |
| 18. #11745148 | C22 | semidirect |
| 19. D464 | C22 | semidirect |
| 69. C22×C16 | D29 | semidirect |
| 71. C2×C29 | #508 | semidirect |
| 86. C2×C16 | C2×D29 | semidirect |
| 87. C29 | C2×#508 | semidirect |
| 133. C2 | #14271595 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| #14271595 | 2 |
| C2×Dic232 | 2 |
| C2×#11745148 | 2 |
| C2×D464 | 2 |
| C22×C16×C29 | 2 |
| C2×#508 | 29 |