Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
442 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 105 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. C22×C4×Dic29 | C2 | semidirect |
| 2. C2×#11745185 | C2 | semidirect |
| 3. #14271127 | C2 | semidirect |
| 4. #14270922 | C2 | semidirect |
| 10. C29×C22⋊Q8 | C4 | semidirect |
| 11. C29×#121 | C4 | semidirect |
| 24. C2×Q8×C29 | C2×C4 | semidirect |
| 27. C2×D4×C29 | C2×C4 | semidirect |
| 39. C4⋊C4×C29 | C2×C4 | semidirect |
| 46. C4×Dic29 | D4 | semidirect |
| 85. C22×C29 | #104 | semidirect |
| 111. C22⋊Q8 | Dic29 | semidirect |
| 112. #121 | Dic29 | semidirect |
| 121. C29 | #1896 | semidirect |
| 125. C2×Q8 | C2×Dic29 | semidirect |
| 128. C2×D4 | C2×Dic29 | semidirect |
| 143. C4⋊C4 | C2×Dic29 | semidirect |
| 185. C22 | #11745185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic29 | 2 |
| C2×#11745185 | 2 |
| #14271127 | 2 |
| #14270922 | 2 |
| C29×#525 | 2 |
| #1896 | 29 |