Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
368 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 202 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. #14272222 | C2 | direct (N × H) |
| 2. C2×#11745206 | C2 | semidirect |
| 3. C2×#11745214 | C2 | semidirect |
| 4. C2×D29⋊C16 | C2 | semidirect |
| 5. C22×#90770 | C2 | semidirect |
| 14. #11745214 | C22 | semidirect |
| 18. C2×#90770 | C22 | semidirect |
| 19. #11745206 | C22 | semidirect |
| 20. D29⋊C16 | C22 | semidirect |
| 73. C2×C29 | #504 | semidirect |
| 90. C29 | C2×#504 | semidirect |
| 137. C2 | #14272222 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272222 | 2 |
| C2×#11745206 | 2 |
| C2×#11745214 | 2 |
| C2×D29⋊C16 | 2 |
| C22×#90770 | 2 |
| C2×#11745269 | 2 |
| C2×#504 | 29 |