Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 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×Q8×Dic29 | C2 | semidirect |
| 5. #14271055 | C2 | semidirect |
| 6. #14271028 | C2 | semidirect |
| 7. #14271010 | C2 | semidirect |
| 8. C42×Dic29 | C2 | semidirect |
| 9. C29×#391 | C2 | semidirect |
| 15. #11745309 | C4 | semidirect |
| 33. C2×Q8×C29 | C2×C4 | semidirect |
| 51. #90781 | C2×C4 | semidirect |
| 57. C4×Dic29 | C2×C4 | semidirect |
| 106. Dic29 | #124 | semidirect |
| 110. #391 | D29 | semidirect |
| 142. C29 | C4×#124 | semidirect |
| 146. C2×Q8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745309 | 2 |
| C2×Q8×Dic29 | 2 |
| C2×#11745255 | 2 |
| #14271065 | 2 |
| #14271055 | 2 |
| #14271028 | 2 |
| #14271010 | 2 |
| C42×Dic29 | 2 |
| C29×#391 | 2 |
| C4×#124 | 29 |