Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
510 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×D232 | C2 | semidirect |
| 2. C2×#11745236 | C2 | semidirect |
| 3. C2×#11745169 | C2 | semidirect |
| 4. #14271065 | C2 | semidirect |
| 5. C29×#336 | C2 | semidirect |
| 35. C2×D116 | D4 | semidirect |
| 38. C2×C8×C29 | D4 | semidirect |
| 56. C2×C4×C29 | D8 | semidirect |
| 95. #336 | D29 | semidirect |
| 115. C29 | #2011 | semidirect |
| 137. C2×C8 | D116 | semidirect |
| 163. C2×C4 | D232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| C2×#11745236 | 2 |
| C2×#11745169 | 2 |
| #14271065 | 2 |
| C29×#336 | 2 |
| #2011 | 29 |