Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
474 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 95 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. C22×#90784 | C2 | semidirect |
| 3. C2×#11745169 | C2 | semidirect |
| 4. C2×#11745180 | C2 | semidirect |
| 5. #14271070 | C2 | semidirect |
| 6. #14270917 | C2 | semidirect |
| 7. C22×SD16×C29 | C2 | semidirect |
| 34. C2×Q8×C29 | D4 | semidirect |
| 57. C2×C8×C29 | D4 | semidirect |
| 65. C2×#6597 | D4 | semidirect |
| 99. C2×Dic29 | SD16 | semidirect |
| 130. C22×SD16 | D29 | semidirect |
| 162. C29 | #2014 | semidirect |
| 170. C2×Q8 | C22⋊D29 | semidirect |
| 197. C2×C8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90784 | 2 |
| C2×#11745302 | 2 |
| C2×#11745169 | 2 |
| C2×#11745180 | 2 |
| #14271070 | 2 |
| #14270917 | 2 |
| C22×SD16×C29 | 2 |
| #2014 | 29 |