Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
356 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 153 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. #24923670 | C2 | semidirect |
| 4. #24923669 | C2 | semidirect |
| 5. #24923666 | C2 | semidirect |
| 31. C2×C167⋊C8 | Q8 | semidirect |
| 44. C2×C8×C167 | Q8 | semidirect |
| 78. C167 | #3160 | semidirect |
| 114. C2×C8 | Dic334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923822 | 2 |
| #24923673 | 2 |
| #24923670 | 2 |
| #24923669 | 2 |
| #24923666 | 2 |
| #24923307 | 2 |
| #24923305 | 2 |
| C2×C8×Dic167 | 2 |
| #427×C167 | 2 |
| #3160 | 167 |