Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
908 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 245 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×#90779 | C2 | semidirect |
| 3. #14271087 | C2 | direct (N × H) |
| 4. C2×C29×#95 | C2 | semidirect |
| 11. C2×#90779 | C22 | semidirect |
| 12. C29×#95 | C22 | semidirect |
| 62. C2×#95 | D29 | semidirect |
| 63. C2×C29 | #396 | semidirect |
| 75. #95 | C2×D29 | semidirect |
| 76. C29 | C2×#396 | semidirect |
| 123. C2 | #14271087 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90779 | 2 |
| C22×#90781 | 2 |
| #14271087 | 2 |
| C2×C29×#95 | 2 |
| C2×#396 | 29 |