Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
408 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 121 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. C22×#90777 | C2 | semidirect |
| 2. C2×C22⋊#6597 | C2 | semidirect |
| 3. C2×C22⋊#6597 | C2 | semidirect |
| 4. #14270918 | C2 | semidirect |
| 50. C2×#6597 | D4 | semidirect |
| 60. C23×C29 | M16 | semidirect |
| 77. C2×C4×C29 | M16 | semidirect |
| 134. C29 | #1870 | semidirect |
| 173. C23 | #90777 | semidirect |
| 190. C2×C4 | #90777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90777 | 2 |
| C2×C22⋊#6597 | 2 |
| #14270918 | 2 |
| C2×C4×D4×C29 | 2 |
| #1870 | 29 |