Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
578 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 578 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. #14271638 | C2 | semidirect |
| 3. #14271018 | C2 | semidirect |
| 4. #14270929 | C2 | semidirect |
| 5. C2×C29×#99 | C2 | semidirect |
| 14. #11745299 | C4 | semidirect |
| 27. C23×D29 | C2×C4 | semidirect |
| 38. C22×Dic29 | D4 | semidirect |
| 45. C22⋊Dic29 | C2×C4 | semidirect |
| 54. C23×C29 | C22⋊C4 | semidirect |
| 78. C2×C4×C29 | C22⋊C4 | semidirect |
| 114. C2×#99 | D29 | semidirect |
| 139. C29 | #1889 | semidirect |
| 186. C23 | #90781 | semidirect |
| 204. C2×C4 | #90781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745299 | 2 |
| #14271638 | 2 |
| #14271018 | 2 |
| #14270929 | 2 |
| C2×C29×#99 | 2 |
| #1889 | 29 |