Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
528 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 234 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. #14272181 | C2 | direct (N × H) |
| 2. C2×#11745220 | C2 | semidirect |
| 4. C2×C4×#6599 | C2 | semidirect |
| 16. #11745220 | C22 | semidirect |
| 18. C4×#6599 | C22 | semidirect |
| 28. C2×C4×D29 | C8 | semidirect |
| 62. C4×D29 | C2×C8 | semidirect |
| 85. C2×C29 | #431 | semidirect |
| 103. C29 | C2×#431 | semidirect |
| 165. C2 | #14272181 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272181 | 2 |
| C2×#11745220 | 2 |
| C2×#11745219 | 2 |
| C2×C4×#6599 | 2 |
| C2×C42×D29 | 2 |
| C2×#431 | 29 |