Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
712 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. #14271029 | C2 | semidirect |
| 4. #14271028 | C2 | semidirect |
| 5. #14271027 | C2 | semidirect |
| 7. C29×#382 | C2 | semidirect |
| 18. C42×D29 | C4 | semidirect |
| 37. C42×C29 | C2×C4 | semidirect |
| 40. C4×Dic29 | C2×C4 | semidirect |
| 41. C4×Dic29 | C2×C4 | semidirect |
| 84. #382 | D29 | direct (N × H) |
| 90. D29 | #382 | direct (N × H) |
| 105. C29 | C2×#382 | semidirect |
| 125. C42 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D29 | 2 |
| C2×C42×D29 | 2 |
| #14271029 | 2 |
| #14271028 | 2 |
| #14271027 | 2 |
| #95×D29 | 2 |
| C29×#382 | 2 |
| C2×#382 | 29 |