Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 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×#11745156 | C2 | semidirect |
| 4. #14270925 | C2 | semidirect |
| 16. C22⋊#6597 | C4 | semidirect |
| 39. C2×#6597 | C2×C4 | semidirect |
| 75. C22×C29 | #106 | semidirect |
| 114. C29 | #1853 | semidirect |
| 171. C22 | #11745156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745156 | 2 |
| C2×C22⋊#6597 | 2 |
| #14271023 | 2 |
| #14270925 | 2 |
| C22×C4⋊C4×C29 | 2 |
| #1853 | 29 |