Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1168 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 209 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. C22×#90781 | C2 | semidirect |
| 3. C2×#11745179 | C2 | semidirect |
| 4. C2×C29×#95 | C2 | semidirect |
| 12. C22×D116 | C4 | semidirect |
| 36. C22×C4×C29 | D4 | semidirect |
| 41. C22×Dic29 | D4 | semidirect |
| 75. C22×D29 | C22⋊C4 | semidirect |
| 84. C2×C4×C29 | C22⋊C4 | semidirect |
| 123. C2×#95 | D29 | semidirect |
| 146. C29 | #1438 | semidirect |
| 173. C22×C4 | D116 | semidirect |
| 219. C2×C4 | #90781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D116 | 2 |
| C22×#90781 | 2 |
| C2×#11745179 | 2 |
| C2×C29×#95 | 2 |
| #1438 | 29 |