Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
516 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745238 | C2 | semidirect |
| 3. #14271058 | C2 | semidirect |
| 4. #14271057 | C2 | semidirect |
| 5. #14271053 | C2 | semidirect |
| 6. C42×Dic29 | C2 | semidirect |
| 7. C2×C29×#126 | C2 | semidirect |
| 32. C42×C29 | D4 | semidirect |
| 75. Dic29 | #126 | semidirect |
| 77. C2×#126 | D29 | semidirect |
| 102. C29 | #2860 | semidirect |
| 120. C42 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745238 | 2 |
| #14271063 | 2 |
| #14271058 | 2 |
| #14271057 | 2 |
| #14271053 | 2 |
| C42×Dic29 | 2 |
| C2×C29×#126 | 2 |
| #2860 | 29 |