Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 380 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. #14271636 | C2 | semidirect |
| 3. C2×#11745182 | C2 | semidirect |
| 4. C2×#11745154 | C2 | semidirect |
| 5. #14270930 | C2 | semidirect |
| 6. #14270929 | C2 | semidirect |
| 7. C2×C29×#99 | C2 | semidirect |
| 12. #11745315 | C4 | semidirect |
| 19. #11745291 | C4 | semidirect |
| 27. C24×C29 | C2×C4 | semidirect |
| 38. C22×C4×C29 | C2×C4 | semidirect |
| 54. C22⋊C4×C29 | D4 | semidirect |
| 60. C22⋊Dic29 | C2×C4 | semidirect |
| 61. C22⋊Dic29 | D4 | semidirect |
| 143. C2×#99 | D29 | semidirect |
| 175. C29 | #1913 | semidirect |
| 177. C24 | C4×D29 | semidirect |
| 199. C22×C4 | C4×D29 | semidirect |
| 214. C22⋊C4 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271722 | 2 |
| #14271636 | 2 |
| C2×#11745182 | 2 |
| C2×#11745154 | 2 |
| #14270930 | 2 |
| #14270929 | 2 |
| C2×C29×#99 | 2 |
| #1913 | 29 |