Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 2. #14271543 | C2 | semidirect |
| 3. #14271515 | C2 | semidirect |
| 5. #14271257 | C2 | semidirect |
| 7. C29×#500 | C2 | semidirect |
| 57. C4×D29 | Q16 | semidirect |
| 75. #500 | D29 | semidirect |
| 101. C29 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271718 | 2 |
| #14271543 | 2 |
| #14271515 | 2 |
| #14271405 | 2 |
| #14271257 | 2 |
| C4×C8×D29 | 2 |
| C29×#500 | 2 |
| #3170 | 29 |