Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14271714 | C2 | semidirect |
| 2. #14271540 | C2 | semidirect |
| 3. #14271511 | C2 | semidirect |
| 4. #14271400 | C2 | semidirect |
| 5. #14271245 | C2 | semidirect |
| 6. C4×C8×D29 | C2 | semidirect |
| 7. C29×#500 | C2 | semidirect |
| 63. C4×D29 | D8 | semidirect |
| 64. C8×C29 | #41 | semidirect |
| 82. #500 | D29 | semidirect |
| 109. C29 | #3169 | semidirect |
| 151. C8 | #90809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271714 | 2 |
| #14271540 | 2 |
| #14271511 | 2 |
| #14271400 | 2 |
| #14271245 | 2 |
| C4×C8×D29 | 2 |
| C29×#500 | 2 |
| #3169 | 29 |