Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 115 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×Q8×Dic29 | C2 | semidirect |
| 2. C2×#11745183 | C2 | semidirect |
| 5. #14270926 | C2 | semidirect |
| 6. #14270917 | C2 | semidirect |
| 12. C2×SD16×C29 | C4 | semidirect |
| 73. Q8×C29 | C22⋊C4 | semidirect |
| 98. C2×Dic29 | SD16 | semidirect |
| 144. C2×SD16 | Dic29 | semidirect |
| 158. C29 | #1880 | semidirect |
| 206. Q8 | C22⋊Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic29 | 2 |
| C2×#11745183 | 2 |
| C2×#11745180 | 2 |
| #14271066 | 2 |
| #14270926 | 2 |
| #14270917 | 2 |
| C22×SD16×C29 | 2 |
| #1880 | 29 |