Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
560 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 2. C2×#11745288 | C2 | semidirect |
| 3. #14271103 | C2 | semidirect |
| 4. #14271100 | C2 | semidirect |
| 5. #14271095 | C2 | semidirect |
| 6. #14271090 | C2 | semidirect |
| 7. #14271088 | C2 | semidirect |
| 9. C4×C4⋊Dic29 | C2 | semidirect |
| 10. C4×#90781 | C2 | semidirect |
| 11. C4×C22⋊C4×C29 | C2 | semidirect |
| 141. C4×C22⋊C4 | D29 | semidirect |
| 174. C29 | #2395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D29 | 2 |
| C2×#11745288 | 2 |
| #14271103 | 2 |
| #14271100 | 2 |
| #14271095 | 2 |
| #14271090 | 2 |
| #14271088 | 2 |
| #14271079 | 2 |
| C4×C4⋊Dic29 | 2 |
| C4×#90781 | 2 |
| C4×C22⋊C4×C29 | 2 |
| #2395 | 29 |