Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
688 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 189 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×#11745291 | C2 | semidirect |
| 3. #14271065 | C2 | semidirect |
| 4. #14271061 | C2 | semidirect |
| 5. #14271054 | C2 | semidirect |
| 6. #14271042 | C2 | semidirect |
| 7. #14271023 | C2 | semidirect |
| 8. C22×C42×C29 | C2 | semidirect |
| 36. C22×C4×C29 | D4 | semidirect |
| 108. C4×C29 | #123 | semidirect |
| 113. C22×C42 | D29 | semidirect |
| 145. C29 | #2854 | semidirect |
| 160. C22×C4 | D116 | semidirect |
| 227. C4 | #11745291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745291 | 2 |
| C2×#11745292 | 2 |
| #14271065 | 2 |
| #14271061 | 2 |
| #14271054 | 2 |
| #14271042 | 2 |
| #14271023 | 2 |
| C22×C42×C29 | 2 |
| #2854 | 29 |