Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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. #14271637 | C2 | semidirect |
| 3. #14271181 | C2 | semidirect |
| 4. #14271179 | C2 | semidirect |
| 5. C2×#11745171 | C2 | semidirect |
| 6. #14270919 | C2 | semidirect |
| 7. C29×H(3,ℤ/4) | C2 | semidirect |
| 19. #11745237 | C4 | semidirect |
| 20. #11745236 | C4 | semidirect |
| 38. C2×D116 | C2×C4 | semidirect |
| 42. C2×Dic58 | C2×C4 | semidirect |
| 50. C42×C29 | C2×C4 | semidirect |
| 51. C42×C29 | D4 | semidirect |
| 56. C4×Dic29 | D4 | semidirect |
| 117. H(3,ℤ/4) | D29 | semidirect |
| 141. C29 | #1911 | semidirect |
| 175. C42 | C4×D29 | semidirect |
| 176. C42 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271732 | 2 |
| #14271637 | 2 |
| #14271181 | 2 |
| #14271179 | 2 |
| C2×#11745171 | 2 |
| #14270919 | 2 |
| C29×H(3,ℤ/4) | 2 |
| #1911 | 29 |