Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 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×D8×D29 | C2 | semidirect |
| 2. #127×D29 | C2 | semidirect |
| 3. #14271540 | C2 | semidirect |
| 4. #14271539 | C2 | semidirect |
| 5. #14271538 | C2 | semidirect |
| 6. C4×C8×D29 | C2 | semidirect |
| 7. C29×#493 | C2 | semidirect |
| 10. C2×D8×C29 | C22 | semidirect |
| 11. C29×#127 | C22 | semidirect |
| 13. #11745302 | C22 | semidirect |
| 14. C2×#90782 | C22 | semidirect |
| 16. C2×D232 | C22 | semidirect |
| 18. #11745236 | C22 | semidirect |
| 20. C4×C8×C29 | C22 | semidirect |
| 21. C8×Dic29 | C22 | semidirect |
| 22. C4×#6597 | C22 | semidirect |
| 42. C8×D29 | D4 | semidirect |
| 58. C4×D29 | D8 | semidirect |
| 60. C8×C29 | C2×D4 | semidirect |
| 61. #6597 | C2×D4 | semidirect |
| 71. C4×C29 | C2×D8 | semidirect |
| 74. Dic29 | C2×D8 | semidirect |
| 80. #493 | D29 | direct (N × H) |
| 86. D29 | #493 | direct (N × H) |
| 92. C2×D8 | C2×D29 | semidirect |
| 97. #127 | C2×D29 | semidirect |
| 101. C4×C8 | C2×D29 | semidirect |
| 102. C29 | C2×#493 | semidirect |
| 141. C8 | D4×D29 | semidirect |
| 152. C4 | D8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D29 | 2 |
| #127×D29 | 2 |
| #14271540 | 2 |
| #14271539 | 2 |
| #14271538 | 2 |
| C4×C8×D29 | 2 |
| C29×#493 | 2 |
| C2×#493 | 29 |