Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #14271513 | C2 | semidirect |
| 3. #14271496 | C2 | semidirect |
| 4. #14271458 | C2 | semidirect |
| 5. #14271402 | C2 | semidirect |
| 6. #14271370 | C2 | semidirect |
| 7. #14271319 | C2 | semidirect |
| 8. C4×#90785 | C2 | semidirect |
| 10. C2×#11745183 | C2 | semidirect |
| 82. D4×C29 | Q16 | semidirect |
| 163. C29 | #3299 | semidirect |
| 208. D4 | #90785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271870 | 2 |
| #14271513 | 2 |
| #14271496 | 2 |
| #14271458 | 2 |
| #14271402 | 2 |
| #14271370 | 2 |
| #14271319 | 2 |
| C4×#90785 | 2 |
| D4×#6597 | 2 |
| C2×#11745183 | 2 |
| D4×Q8×C29 | 2 |
| #3299 | 29 |