Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×C22⋊#6597 | C2 | semidirect |
| 2. #14270887 | C2 | direct (N × H) |
| 13. C22⋊#6597 | C22 | semidirect |
| 19. C24×C29 | C8 | semidirect |
| 52. C23×C29 | C2×C8 | semidirect |
| 97. C2×C29 | #323 | semidirect |
| 111. C29 | C2×#323 | semidirect |
| 117. C24 | #6597 | semidirect |
| 148. C23 | C2×#6597 | semidirect |
| 191. C2 | #14270887 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#6597 | 2 |
| #14270887 | 2 |
| C22×C22⋊C4×C29 | 2 |
| C2×#323 | 29 |