Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
584 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C22×#90784 | C2 | semidirect |
| 3. C2×Q8×Dic29 | C2 | semidirect |
| 4. #14271361 | C2 | direct (N × H) |
| 5. C2×#11745162 | C2 | semidirect |
| 6. C2×#11745169 | C2 | semidirect |
| 7. C2×#11745180 | C2 | semidirect |
| 8. C22×SD16×C29 | C2 | semidirect |
| 15. C2×SD16×C29 | C22 | semidirect |
| 18. Q8×Dic29 | C22 | semidirect |
| 20. C2×#90784 | C22 | semidirect |
| 28. #11745180 | C22 | semidirect |
| 29. #11745169 | C22 | semidirect |
| 30. #11745162 | C22 | semidirect |
| 35. C2×Q8×C29 | D4 | semidirect |
| 77. Q8×C29 | C2×D4 | semidirect |
| 92. C2×Dic29 | SD16 | semidirect |
| 119. Dic29 | C2×SD16 | semidirect |
| 121. C22×SD16 | D29 | semidirect |
| 129. C2×C29 | #460 | semidirect |
| 142. C2×SD16 | C2×D29 | semidirect |
| 156. C29 | C2×#460 | semidirect |
| 161. C2×Q8 | C22⋊D29 | semidirect |
| 203. Q8 | C2×C22⋊D29 | semidirect |
| 247. C2 | #14271361 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90784 | 2 |
| C2×#11745302 | 2 |
| C2×Q8×Dic29 | 2 |
| #14271361 | 2 |
| C2×#11745162 | 2 |
| C2×#11745169 | 2 |
| C2×#11745180 | 2 |
| C22×SD16×C29 | 2 |
| C2×#460 | 29 |