Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 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. #14271491 | C2 | semidirect |
| 4. #14271448 | C2 | semidirect |
| 5. #14271394 | C2 | semidirect |
| 6. #14271365 | C2 | semidirect |
| 7. #14271302 | C2 | semidirect |
| 8. C4×#90784 | C2 | semidirect |
| 9. D4×#6597 | C2 | semidirect |
| 10. C2×#11745183 | C2 | semidirect |
| 11. D4×Q8×C29 | C2 | semidirect |
| 83. Q8×C29 | #41 | semidirect |
| 84. D4×C29 | SD16 | semidirect |
| 124. D4×Q8 | D29 | semidirect |
| 169. C29 | #3298 | semidirect |
| 213. Q8 | #90807 | semidirect |
| 217. D4 | #90784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271817 | 2 |
| #14271513 | 2 |
| #14271491 | 2 |
| #14271448 | 2 |
| #14271394 | 2 |
| #14271365 | 2 |
| #14271302 | 2 |
| C4×#90784 | 2 |
| D4×#6597 | 2 |
| C2×#11745183 | 2 |
| D4×Q8×C29 | 2 |
| #3298 | 29 |