Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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. #14271963 | C2 | semidirect |
| 2. #14271675 | C2 | semidirect |
| 3. #14271181 | C2 | semidirect |
| 4. #14271126 | C2 | semidirect |
| 5. C29×H(3,ℤ/4) | C2 | semidirect |
| 30. C2×D116 | D4 | semidirect |
| 36. C2×Dic58 | D4 | semidirect |
| 38. C2×C8×C29 | D4 | semidirect |
| 41. C42×C29 | D4 | semidirect |
| 98. H(3,ℤ/4) | D29 | semidirect |
| 119. C29 | #2010 | semidirect |
| 142. C2×C8 | D116 | semidirect |
| 148. C42 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271963 | 2 |
| #14271675 | 2 |
| #14271181 | 2 |
| #14271126 | 2 |
| C29×H(3,ℤ/4) | 2 |
| #2010 | 29 |