Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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. #24923673 | C2 | semidirect |
| 3. #24923647 | C2 | semidirect |
| 4. #24923618 | C2 | semidirect |
| 8. C4×Dic668 | C2 | semidirect |
| 9. C4×#14581940 | C2 | semidirect |
| 11. C4×Q16×C167 | C2 | semidirect |
| 83. C4×D167 | Q16 | semidirect |
| 114. C167 | #3170 | semidirect |
| 125. C4×Q16 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923823 | 2 |
| #24923673 | 2 |
| #24923647 | 2 |
| #24923618 | 2 |
| #24923511 | 2 |
| #24923509 | 2 |
| #24923507 | 2 |
| C4×Dic668 | 2 |
| C4×#14581940 | 2 |
| C4×C8×D167 | 2 |
| C4×Q16×C167 | 2 |
| #3170 | 167 |