Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
740 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 155 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×Q16×D29 | C2 | semidirect |
| 4. #14271321 | C2 | semidirect |
| 5. #14271320 | C2 | semidirect |
| 6. #14271319 | C2 | semidirect |
| 7. #14271318 | C2 | semidirect |
| 8. #14271317 | C2 | semidirect |
| 9. #103×D29 | C2 | semidirect |
| 11. C29×#451 | C2 | semidirect |
| 23. C2×Q16×C29 | C22 | semidirect |
| 26. C2×#90785 | C22 | semidirect |
| 27. C2×#90785 | C22 | semidirect |
| 30. C2×Dic116 | C22 | semidirect |
| 38. C29×#103 | C22 | semidirect |
| 40. #11745183 | C22 | semidirect |
| 43. #11745164 | C22 | semidirect |
| 44. #11745158 | C22 | semidirect |
| 100. C22×D29 | Q16 | semidirect |
| 141. C22×C29 | C2×Q16 | semidirect |
| 148. C2×D29 | C2×Q16 | semidirect |
| 168. #451 | D29 | direct (N × H) |
| 176. D29 | #451 | direct (N × H) |
| 192. C2×Q16 | C2×D29 | semidirect |
| 206. #103 | C2×D29 | semidirect |
| 210. C29 | C2×#451 | semidirect |
| 313. C22 | Q16×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D29 | 2 |
| C2×Q16×D29 | 2 |
| C22⋊Q8×D29 | 2 |
| #14271321 | 2 |
| #14271320 | 2 |
| #14271319 | 2 |
| #14271318 | 2 |
| #14271317 | 2 |
| #103×D29 | 2 |
| C22⋊C8×D29 | 2 |
| C29×#451 | 2 |
| C2×#451 | 29 |