Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
552 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 245 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. C2×Q8×Dic29 | C2 | semidirect |
| 3. SD16×Dic29 | C2 | direct (N × H) |
| 4. C2×#11745165 | C2 | semidirect |
| 5. C2×#11745183 | C2 | semidirect |
| 7. C2×C8×Dic29 | C2 | semidirect |
| 12. C2×SD16×C29 | C4 | semidirect |
| 17. Q8×Dic29 | C22 | semidirect |
| 26. #11745183 | C22 | semidirect |
| 28. #11745165 | C22 | semidirect |
| 29. C8×Dic29 | C22 | semidirect |
| 33. C2×Q8×C29 | C2×C4 | semidirect |
| 47. SD16×C29 | C2×C4 | semidirect |
| 48. C2×C8×C29 | C2×C4 | semidirect |
| 68. Q8×C29 | C22×C4 | semidirect |
| 84. C2×Dic29 | SD16 | direct (N × H) |
| 87. C8×C29 | C22×C4 | semidirect |
| 105. Dic29 | C2×SD16 | direct (N × H) |
| 115. C2×C29 | C4×SD16 | semidirect |
| 122. C2×SD16 | Dic29 | direct (N × H) |
| 140. C29 | C2×C4×SD16 | semidirect |
| 144. C2×Q8 | C2×Dic29 | semidirect |
| 158. SD16 | C2×Dic29 | direct (N × H) |
| 161. C2×C8 | C2×Dic29 | semidirect |
| 179. Q8 | C22×Dic29 | semidirect |
| 199. C8 | C22×Dic29 | semidirect |
| 217. C2 | SD16×Dic29 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic29 | 2 |
| C2×D4×Dic29 | 2 |
| SD16×Dic29 | 2 |
| C2×#11745165 | 2 |
| C2×#11745183 | 2 |
| C2×#11745180 | 2 |
| C2×C8×Dic29 | 2 |
| C22×SD16×C29 | 2 |
| C2×C4×SD16 | 29 |