Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic58 | C2 | semidirect |
| 3. #14271514 | C2 | semidirect |
| 4. #14271494 | C2 | semidirect |
| 5. #14271449 | C2 | semidirect |
| 6. #14271392 | C2 | semidirect |
| 7. #14271369 | C2 | semidirect |
| 8. #14271304 | C2 | semidirect |
| 9. C4×#90773 | C2 | semidirect |
| 10. C2×#11745164 | C2 | semidirect |
| 11. C8×D4×C29 | C2 | semidirect |
| 79. D4×C29 | SD16 | semidirect |
| 102. Dic58 | #41 | semidirect |
| 133. C8×D4 | D29 | semidirect |
| 169. C29 | #3298 | semidirect |
| 217. D4 | #90773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic58 | 2 |
| #14271817 | 2 |
| #14271514 | 2 |
| #14271494 | 2 |
| #14271449 | 2 |
| #14271392 | 2 |
| #14271369 | 2 |
| #14271304 | 2 |
| C4×#90773 | 2 |
| C2×#11745164 | 2 |
| C8×D4×C29 | 2 |
| #3298 | 29 |