Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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. #14271566 | C2 | semidirect |
| 3. #14271536 | C2 | semidirect |
| 4. #14271511 | C2 | semidirect |
| 5. #14271509 | C2 | semidirect |
| 6. C8×#6597 | C2 | semidirect |
| 7. C29×#492 | C2 | semidirect |
| 55. C8×C29 | D8 | semidirect |
| 57. #6597 | SD16 | semidirect |
| 74. #492 | D29 | semidirect |
| 96. C29 | #1706 | semidirect |
| 133. C8 | #90782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271566 | 2 |
| #14271539 | 2 |
| #14271536 | 2 |
| #14271511 | 2 |
| #14271509 | 2 |
| C8×#6597 | 2 |
| C29×#492 | 2 |
| #1706 | 29 |