Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 181 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. #24923398 | C2 | semidirect |
| 3. #24923396 | C2 | semidirect |
| 33. C2×C167⋊C8 | Q8 | semidirect |
| 83. C167 | #2961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923822 | 2 |
| #24923398 | 2 |
| #24923396 | 2 |
| #24923295 | 2 |
| #24923292 | 2 |
| #24923227 | 2 |
| #24923225 | 2 |
| C2×#19128742 | 2 |
| #424×C167 | 2 |
| #2961 | 167 |