Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 145 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. #14271566 | C2 | semidirect |
| 3. #14271539 | C2 | semidirect |
| 4. #14271511 | C2 | semidirect |
| 5. #14271509 | C2 | semidirect |
| 6. #14271397 | C2 | semidirect |
| 7. C4×#90782 | C2 | semidirect |
| 8. C2×C4×#6597 | C2 | semidirect |
| 9. C29×#532 | C2 | semidirect |
| 80. C2×C4×C29 | D8 | semidirect |
| 95. #6597 | #41 | semidirect |
| 116. #532 | D29 | semidirect |
| 155. C29 | #3169 | semidirect |
| 208. C2×C4 | #90782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271713 | 2 |
| #14271566 | 2 |
| #14271539 | 2 |
| #14271511 | 2 |
| #14271509 | 2 |
| #14271397 | 2 |
| C4×#90782 | 2 |
| C2×C4×#6597 | 2 |
| C29×#532 | 2 |
| #3169 | 29 |