Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
152 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 42. C8×C167 | Q16 | semidirect |
| 54. C167 | #1694 | semidirect |
| 97. C8 | #14581940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923674 | 2 |
| #24923479 | 2 |
| #24923020 | 2 |
| #24923014 | 2 |
| #446×C167 | 2 |
| #1694 | 167 |