Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 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. #14271509 | C2 | semidirect |
| 2. #14271443 | C2 | semidirect |
| 3. #14271368 | C2 | semidirect |
| 4. #14270907 | C2 | semidirect |
| 5. D4⋊#6597 | C2 | semidirect |
| 6. D4⋊#6597 | C2 | semidirect |
| 17. #11745231 | C22 | semidirect |
| 22. C4⋊#6597 | C22 | semidirect |
| 23. C4⋊#6597 | C22 | semidirect |
| 24. C4×#6597 | C22 | semidirect |
| 68. D4×C29 | SD16 | semidirect |
| 134. C29 | #1639 | semidirect |
| 180. D4 | #90783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271509 | 2 |
| #14271443 | 2 |
| #14271368 | 2 |
| #14270907 | 2 |
| D4⋊#6597 | 2 |
| D42×C29 | 2 |
| #1639 | 29 |