Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
232 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 4. #14270968 | C2 | semidirect |
| 5. #14270967 | C2 | semidirect |
| 6. #14270966 | C2 | semidirect |
| 7. C29×#358 | C2 | semidirect |
| 12. Q16×D29 | C4 | semidirect |
| 31. Q16×C29 | C2×C4 | semidirect |
| 39. Dic116 | C2×C4 | semidirect |
| 81. #358 | D29 | direct (N × H) |
| 85. D29 | #358 | direct (N × H) |
| 100. C29 | C2×#358 | semidirect |
| 113. Q16 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D29 | 2 |
| C2×C16×D29 | 2 |
| #107×D29 | 2 |
| #14270968 | 2 |
| #14270967 | 2 |
| #14270966 | 2 |
| C29×#358 | 2 |
| C2×#358 | 29 |