Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
552 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 205 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×Q8×Dic29 | C2 | semidirect |
| 4. #14271248 | C2 | direct (N × H) |
| 5. C2×#11745156 | C2 | semidirect |
| 7. C2×C8×Dic29 | C2 | semidirect |
| 8. C2×C29×#103 | C2 | semidirect |
| 15. Q8×Dic29 | C22 | semidirect |
| 16. C2×#90784 | C4 | semidirect |
| 26. C29×#103 | C22 | semidirect |
| 28. C8×Dic29 | C22 | semidirect |
| 29. #11745156 | C22 | semidirect |
| 33. C2×Q8×C29 | C2×C4 | semidirect |
| 51. #90784 | C2×C4 | semidirect |
| 59. C2×#6597 | C2×C4 | semidirect |
| 68. Q8×C29 | C22×C4 | semidirect |
| 80. C2×Dic29 | SD16 | semidirect |
| 88. #6597 | C22×C4 | semidirect |
| 105. Dic29 | C2×SD16 | semidirect |
| 111. C2×#103 | D29 | semidirect |
| 114. C2×C29 | C4×SD16 | semidirect |
| 137. #103 | C2×D29 | semidirect |
| 140. C29 | C2×C4×SD16 | semidirect |
| 144. C2×Q8 | C4×D29 | semidirect |
| 179. Q8 | C2×C4×D29 | semidirect |
| 217. C2 | #14271248 | 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×Q8×Dic29 | 2 |
| C2×#11745255 | 2 |
| #14271248 | 2 |
| C2×#11745156 | 2 |
| C2×#11745169 | 2 |
| C2×C8×Dic29 | 2 |
| C2×C29×#103 | 2 |
| C2×C4×SD16 | 29 |