Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
568 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 157 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×C4×Dic58 | C2 | semidirect |
| 3. #14271103 | C2 | semidirect |
| 4. #14271090 | C2 | semidirect |
| 6. #14271076 | C2 | semidirect |
| 7. C4×#90781 | C2 | semidirect |
| 8. C29×#376 | C2 | semidirect |
| 99. #376 | D29 | semidirect |
| 123. C29 | #2398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic58 | 2 |
| C2×C4×D116 | 2 |
| #14271103 | 2 |
| #14271090 | 2 |
| #14271081 | 2 |
| #14271076 | 2 |
| C4×#90781 | 2 |
| C29×#376 | 2 |
| #2398 | 29 |