Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
336 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 109 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. #14270900 | C2 | direct (N × H) |
| 5. C22×Q8×C29 | C4 | semidirect |
| 10. C29×C22⋊Q8 | C4 | semidirect |
| 13. C2×C4⋊C4×C29 | C4 | semidirect |
| 23. C2×Q8×C29 | C2×C4 | semidirect |
| 40. C4⋊C4×C29 | C2×C4 | semidirect |
| 101. C2×C29 | #328 | semidirect |
| 105. C22×Q8 | Dic29 | semidirect |
| 111. C22⋊Q8 | Dic29 | semidirect |
| 114. C2×C4⋊C4 | Dic29 | semidirect |
| 120. C29 | C2×#328 | semidirect |
| 124. C2×Q8 | C2×Dic29 | semidirect |
| 143. C4⋊C4 | C2×Dic29 | semidirect |
| 197. C2 | #14270900 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#6597 | 2 |
| C2×#11745179 | 2 |
| #14270900 | 2 |
| C2×C29×C22⋊Q8 | 2 |
| C2×#328 | 29 |