Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 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×D116 | C2 | semidirect |
| 2. #14271540 | C2 | semidirect |
| 3. #14271359 | C2 | semidirect |
| 4. #14271358 | C2 | semidirect |
| 5. #14270906 | C2 | semidirect |
| 6. #14270892 | C2 | semidirect |
| 7. C29×D4⋊C8 | C2 | semidirect |
| 18. #11745236 | C22 | semidirect |
| 20. C29×C4⋊C8 | C22 | semidirect |
| 21. C4×C8×C29 | C22 | semidirect |
| 24. C4⋊#6597 | C22 | semidirect |
| 62. D4×C29 | D8 | semidirect |
| 83. D116 | D8 | semidirect |
| 117. D4⋊C8 | D29 | semidirect |
| 138. C4⋊C8 | C2×D29 | semidirect |
| 141. C4×C8 | C2×D29 | semidirect |
| 142. C29 | #1619 | semidirect |
| 194. D4 | D232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D116 | 2 |
| #14271540 | 2 |
| #14271359 | 2 |
| #14271358 | 2 |
| #14270906 | 2 |
| #14270892 | 2 |
| C29×D4⋊C8 | 2 |
| #1619 | 29 |