Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
280 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 97 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. #14270895 | C2 | semidirect |
| 5. Q8⋊#6597 | C2 | semidirect |
| 6. #14270893 | C2 | semidirect |
| 7. C29×Q8⋊C8 | C2 | semidirect |
| 29. Q8×D29 | C8 | semidirect |
| 60. Q8×C29 | C2×C8 | semidirect |
| 80. Dic58 | C2×C8 | semidirect |
| 108. Q8⋊C8 | D29 | direct (N × H) |
| 112. D29 | Q8⋊C8 | direct (N × H) |
| 132. C29 | C2×Q8⋊C8 | semidirect |
| 169. Q8 | C8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D29 | 2 |
| C4⋊C8×D29 | 2 |
| C4×C8×D29 | 2 |
| #14270895 | 2 |
| Q8⋊#6597 | 2 |
| #14270893 | 2 |
| C29×Q8⋊C8 | 2 |
| C2×Q8⋊C8 | 29 |