Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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. #14271536 | C2 | semidirect |
| 2. #14271443 | C2 | semidirect |
| 4. #14270914 | C2 | semidirect |
| 5. #14270910 | C2 | semidirect |
| 6. #14270906 | C2 | semidirect |
| 7. C8×D4×C29 | C2 | semidirect |
| 46. D4×C29 | SD16 | semidirect |
| 63. C8×C29 | D8 | semidirect |
| 84. C8×D4 | D29 | semidirect |
| 108. C29 | #1665 | semidirect |
| 139. D4 | #90773 | semidirect |
| 151. C8 | #90782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271536 | 2 |
| #14271443 | 2 |
| #14271358 | 2 |
| #14270914 | 2 |
| #14270910 | 2 |
| #14270906 | 2 |
| C8×D4×C29 | 2 |
| #1665 | 29 |