Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. #24923992 | C2 | semidirect |
| 3. #24923648 | C2 | semidirect |
| 4. #24923491 | C2 | semidirect |
| 5. #24923488 | C2 | semidirect |
| 6. #24923474 | C2 | semidirect |
| 7. #24923471 | C2 | semidirect |
| 8. Q8×C167⋊C8 | C2 | semidirect |
| 9. C4×#14581940 | C2 | semidirect |
| 11. #556×C167 | C2 | semidirect |
| 123. C167 | #3393 | semidirect |
| 126. #556 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923992 | 2 |
| #24923651 | 2 |
| #24923648 | 2 |
| #24923491 | 2 |
| #24923488 | 2 |
| #24923474 | 2 |
| #24923471 | 2 |
| Q8×C167⋊C8 | 2 |
| C4×#14581940 | 2 |
| C4×#14581935 | 2 |
| #556×C167 | 2 |
| #3393 | 167 |