Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11745274 | C2 | semidirect |
| 2. #14271711 | C2 | semidirect |
| 3. #14271546 | C2 | semidirect |
| 4. #14271543 | C2 | semidirect |
| 5. #14271535 | C2 | semidirect |
| 6. C4×C8×D29 | C2 | semidirect |
| 7. C29×#493 | C2 | semidirect |
| 41. C8×D29 | D4 | semidirect |
| 64. C4×C29 | #135 | semidirect |
| 73. #493 | D29 | semidirect |
| 95. C29 | #3147 | semidirect |
| 139. C4 | #11745274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745274 | 2 |
| #14271711 | 2 |
| #14271546 | 2 |
| #14271543 | 2 |
| #14271535 | 2 |
| C4×C8×D29 | 2 |
| C29×#493 | 2 |
| #3147 | 29 |