Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
528 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 145 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. C4⋊Q8×D29 | C2 | semidirect |
| 3. #14271511 | C2 | semidirect |
| 4. #14271510 | C2 | semidirect |
| 5. #14271509 | C2 | semidirect |
| 6. #14271508 | C2 | semidirect |
| 7. #102×D29 | C2 | semidirect |
| 8. C4×C8×D29 | C2 | semidirect |
| 9. C29×#486 | C2 | semidirect |
| 14. C29×C4⋊Q8 | C22 | semidirect |
| 24. #11745250 | C22 | semidirect |
| 27. #11745231 | C22 | semidirect |
| 28. C29×#102 | C22 | semidirect |
| 29. C4×C8×C29 | C22 | semidirect |
| 30. #11745180 | C22 | semidirect |
| 31. #11745169 | C22 | semidirect |
| 32. C8×Dic29 | C22 | semidirect |
| 33. #11745157 | C22 | semidirect |
| 34. C4×#6597 | C22 | semidirect |
| 127. #486 | D29 | direct (N × H) |
| 135. D29 | #486 | direct (N × H) |
| 145. C4⋊Q8 | C2×D29 | semidirect |
| 157. #102 | C2×D29 | semidirect |
| 160. C4×C8 | C2×D29 | semidirect |
| 161. C29 | C2×#486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D29 | 2 |
| #127×D29 | 2 |
| #14271511 | 2 |
| #14271510 | 2 |
| #14271509 | 2 |
| #14271508 | 2 |
| #102×D29 | 2 |
| C4×C8×D29 | 2 |
| C29×#486 | 2 |
| C2×#486 | 29 |