Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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. #14271180 | C2 | semidirect |
| 3. C2×#11745153 | C2 | semidirect |
| 4. #14271136 | C2 | semidirect |
| 5. #14270933 | C2 | semidirect |
| 6. #14270923 | C2 | semidirect |
| 7. C4×#41×C29 | C2 | semidirect |
| 17. #11745313 | C4 | semidirect |
| 19. #11745311 | C4 | semidirect |
| 45. C2×D116 | C2×C4 | semidirect |
| 47. C2×Dic58 | C2×C4 | semidirect |
| 67. #90777 | C2×C4 | semidirect |
| 125. C4×#41 | D29 | semidirect |
| 158. C29 | #1906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271961 | 2 |
| #14271180 | 2 |
| C2×#11745153 | 2 |
| #14271136 | 2 |
| #14270933 | 2 |
| #14270923 | 2 |
| C4×#41×C29 | 2 |
| #1906 | 29 |