Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
440 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 440 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 |
|---|---|---|
| 3. #14271212 | C2 | semidirect |
| 4. #14271210 | C2 | semidirect |
| 5. C2×#11745170 | C2 | semidirect |
| 6. #108×D29 | C2 | semidirect |
| 7. C29×#430 | C2 | semidirect |
| 76. #430 | D29 | semidirect |
| 98. C29 | #2916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271929 | 2 |
| C2×#11745269 | 2 |
| #14271212 | 2 |
| #14271210 | 2 |
| C2×#11745170 | 2 |
| #108×D29 | 2 |
| C29×#430 | 2 |
| #2916 | 29 |