Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 149 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. #14271713 | C2 | semidirect |
| 2. #14271568 | C2 | semidirect |
| 3. #14271540 | C2 | semidirect |
| 4. #14271510 | C2 | semidirect |
| 5. #14271399 | C2 | semidirect |
| 6. C4×D232 | C2 | semidirect |
| 7. C2×C4×C8×C29 | C2 | semidirect |
| 50. C2×C4×C29 | D8 | semidirect |
| 65. C8×C29 | #41 | semidirect |
| 87. C2×C4×C8 | D29 | semidirect |
| 109. C29 | #3169 | semidirect |
| 143. C2×C4 | D232 | semidirect |
| 151. C8 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271713 | 2 |
| #14271568 | 2 |
| #14271540 | 2 |
| #14271510 | 2 |
| #14271399 | 2 |
| C4×D232 | 2 |
| C2×C4×C8×C29 | 2 |
| #3169 | 29 |