Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 197 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×#90785 | C2 | semidirect |
| 3. #14271319 | C2 | direct (N × H) |
| 4. C2×#11745183 | C2 | semidirect |
| 17. C2×#90785 | C22 | semidirect |
| 23. #11745183 | C22 | semidirect |
| 56. C23×C29 | Q16 | semidirect |
| 86. C22×C29 | C2×Q16 | semidirect |
| 102. C2×C29 | #451 | semidirect |
| 124. C29 | C2×#451 | semidirect |
| 156. C23 | #90785 | semidirect |
| 185. C22 | C2×#90785 | semidirect |
| 195. C2 | #14271319 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90785 | 2 |
| C2×#11745286 | 2 |
| #14271319 | 2 |
| C2×#11745183 | 2 |
| C2×C22⋊#6597 | 2 |
| C23×Q8×C29 | 2 |
| C2×#451 | 29 |