Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
652 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 229 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. C2×#11745234 | C2 | semidirect |
| 4. #14271061 | C2 | semidirect |
| 5. #14271054 | C2 | semidirect |
| 6. C4×C4⋊Dic29 | C2 | semidirect |
| 7. C4×#90781 | C2 | semidirect |
| 8. C43×C29 | C2 | semidirect |
| 23. C4×D116 | C4 | semidirect |
| 44. C42×C29 | D4 | semidirect |
| 93. C4×C29 | #117 | semidirect |
| 104. C43 | D29 | semidirect |
| 129. C29 | #2293 | semidirect |
| 154. C42 | D116 | semidirect |
| 197. C4 | #11745234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D116 | 2 |
| C2×#11745234 | 2 |
| #14271065 | 2 |
| #14271061 | 2 |
| #14271054 | 2 |
| C4×C4⋊Dic29 | 2 |
| C4×#90781 | 2 |
| C43×C29 | 2 |
| #2293 | 29 |