Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #24923677 | C2 | semidirect |
| 4. #24923676 | C2 | semidirect |
| 5. #24923670 | C2 | semidirect |
| 6. #24923666 | C2 | semidirect |
| 44. C2×C167⋊C8 | Q8 | semidirect |
| 65. M16×C167 | Q8 | semidirect |
| 112. C167 | #3163 | semidirect |
| 159. M16 | Dic334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923900 | 2 |
| #24923897 | 2 |
| #24923677 | 2 |
| #24923676 | 2 |
| #24923670 | 2 |
| #24923666 | 2 |
| #24923311 | 2 |
| #24923305 | 2 |
| C2×#19128763 | 2 |
| #24923227 | 2 |
| #428×C167 | 2 |
| #3163 | 167 |