Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
348 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 34. Q8×C167 | Q16 | semidirect |
| 50. C167 | #3395 | semidirect |
| 83. Q8 | Dic668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923998 | 2 |
| #24923649 | 2 |
| #24923480 | 2 |
| C4×Dic668 | 2 |
| C8×Q8×C167 | 2 |
| #3395 | 167 |