Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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×#11745281 | C2 | semidirect |
| 2. #14271596 | C2 | direct (N × H) |
| 3. C2×#11745176 | C2 | semidirect |
| 4. C2×D464 | C2 | semidirect |
| 5. C2×C16×D29 | C2 | semidirect |
| 6. C2×C29×Q32 | C2 | semidirect |
| 11. #11745281 | C22 | semidirect |
| 14. C29×Q32 | C22 | semidirect |
| 16. #11745176 | C22 | semidirect |
| 18. D464 | C22 | semidirect |
| 19. C16×D29 | C22 | semidirect |
| 66. C2×Q32 | D29 | semidirect |
| 70. C2×C29 | #508 | semidirect |
| 81. Q32 | C2×D29 | semidirect |
| 87. C29 | C2×#508 | semidirect |
| 133. C2 | #14271596 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745281 | 2 |
| #14271596 | 2 |
| C2×#11745176 | 2 |
| C2×D464 | 2 |
| C2×C16×D29 | 2 |
| C2×C29×Q32 | 2 |
| C2×#508 | 29 |