Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#11745151 | C2 | semidirect |
| 4. C2×#11745163 | C2 | semidirect |
| 6. #14270917 | C2 | semidirect |
| 7. C29×#336 | C2 | semidirect |
| 18. C2×C8×D29 | C4 | semidirect |
| 20. #11745168 | C4 | semidirect |
| 80. #6597 | C22⋊C4 | semidirect |
| 91. C2×D29 | #97 | semidirect |
| 105. #336 | D29 | semidirect |
| 127. C29 | #1752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D29 | 2 |
| C2×#11745168 | 2 |
| C2×#11745151 | 2 |
| C2×#11745163 | 2 |
| C4×#90781 | 2 |
| #14270917 | 2 |
| C29×#336 | 2 |
| #1752 | 29 |