Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
656 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 656 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. C2×SD16×D29 | C2 | semidirect |
| 2. C4⋊Q8×D29 | C2 | semidirect |
| 4. #14271537 | C2 | semidirect |
| 5. #14271536 | C2 | semidirect |
| 6. #14271535 | C2 | semidirect |
| 7. #14271534 | C2 | semidirect |
| 8. C4×C8×D29 | C2 | semidirect |
| 9. C29×#492 | C2 | semidirect |
| 13. C2×SD16×C29 | C22 | semidirect |
| 14. C29×C4⋊Q8 | C22 | semidirect |
| 16. #11745306 | C22 | semidirect |
| 17. C2×#90784 | C22 | semidirect |
| 20. C2×#90783 | C22 | semidirect |
| 22. C2×#90773 | C22 | semidirect |
| 28. #11745231 | C22 | semidirect |
| 29. C4×C8×C29 | C22 | semidirect |
| 30. C8×Dic29 | C22 | semidirect |
| 31. C4×#6597 | C22 | semidirect |
| 60. C8×D29 | D4 | semidirect |
| 80. C4×D29 | SD16 | semidirect |
| 84. C8×C29 | C2×D4 | semidirect |
| 85. #6597 | C2×D4 | semidirect |
| 96. C4×C29 | C2×SD16 | semidirect |
| 100. Dic29 | C2×SD16 | semidirect |
| 108. #492 | D29 | direct (N × H) |
| 114. D29 | #492 | direct (N × H) |
| 122. C2×SD16 | C2×D29 | semidirect |
| 127. C4⋊Q8 | C2×D29 | semidirect |
| 136. C4×C8 | C2×D29 | semidirect |
| 137. C29 | C2×#492 | semidirect |
| 191. C8 | D4×D29 | semidirect |
| 204. C4 | SD16×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×D29 | 2 |
| C4⋊Q8×D29 | 2 |
| #127×D29 | 2 |
| #14271537 | 2 |
| #14271536 | 2 |
| #14271535 | 2 |
| #14271534 | 2 |
| C4×C8×D29 | 2 |
| C29×#492 | 2 |
| C2×#492 | 29 |