Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
648 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 648 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×#90782 | C2 | semidirect |
| 2. C2×#11745302 | C2 | semidirect |
| 3. C2×D4×Dic29 | C2 | semidirect |
| 4. #14271356 | C2 | direct (N × H) |
| 5. C2×#11745162 | C2 | semidirect |
| 6. C2×#11745169 | C2 | semidirect |
| 7. C2×#11745180 | C2 | semidirect |
| 8. C22×D8×C29 | C2 | semidirect |
| 16. C2×D8×C29 | C22 | semidirect |
| 20. #11745302 | C22 | semidirect |
| 22. D4×Dic29 | C22 | semidirect |
| 24. C2×#90782 | C22 | semidirect |
| 28. #11745180 | C22 | semidirect |
| 29. #11745169 | C22 | semidirect |
| 30. #11745162 | C22 | semidirect |
| 39. C2×D4×C29 | D4 | semidirect |
| 85. D4×C29 | C2×D4 | semidirect |
| 96. C2×Dic29 | D8 | semidirect |
| 126. Dic29 | C2×D8 | semidirect |
| 128. C22×D8 | D29 | semidirect |
| 137. C2×C29 | #459 | semidirect |
| 151. C2×D8 | C2×D29 | semidirect |
| 164. C29 | C2×#459 | semidirect |
| 181. C2×D4 | C22⋊D29 | semidirect |
| 224. D4 | C2×C22⋊D29 | semidirect |
| 263. C2 | #14271356 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90782 | 2 |
| C2×#11745302 | 2 |
| C2×D4×Dic29 | 2 |
| #14271356 | 2 |
| C2×#11745162 | 2 |
| C2×#11745169 | 2 |
| C2×#11745180 | 2 |
| C22×D8×C29 | 2 |
| C2×#459 | 29 |