Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745231 | C2 | semidirect |
| 2. #14271522 | C2 | direct (N × H) |
| 3. C2×#11745183 | C2 | semidirect |
| 5. C2×#11745151 | C2 | semidirect |
| 19. #11745231 | C22 | semidirect |
| 20. #11745183 | C22 | semidirect |
| 22. #11745151 | C22 | semidirect |
| 90. C2×C29 | #489 | semidirect |
| 110. C29 | C2×#489 | semidirect |
| 171. C2 | #14271522 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745231 | 2 |
| #14271522 | 2 |
| C2×#11745183 | 2 |
| C2×#11745180 | 2 |
| C2×#11745151 | 2 |
| C2×C29×#124 | 2 |
| C2×#489 | 29 |