Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
138 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 53 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. #14271565 | C2 | semidirect |
| 3. #14270968 | C2 | semidirect |
| 5. C4×C16×C29 | C2 | semidirect |
| 51. C4×C16 | D29 | semidirect |
| 64. C29 | #2242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271565 | 2 |
| #14271547 | 2 |
| #14270968 | 2 |
| #14270965 | 2 |
| C4×C16×C29 | 2 |
| #2242 | 29 |