Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#19128864 | C2 | semidirect |
| 3. C2×Q16×D167 | C2 | semidirect |
| 4. #24923844 | C2 | semidirect |
| 5. #24923662 | C2 | semidirect |
| 6. #24923661 | C2 | semidirect |
| 7. #24923654 | C2 | semidirect |
| 8. #24923653 | C2 | semidirect |
| 9. #24923647 | C2 | semidirect |
| 10. #24923223 | C2 | semidirect |
| 11. #494×C167 | C2 | semidirect |
| 121. C167 | #3156 | semidirect |
| 132. #494 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128864 | 2 |
| C2×#19128855 | 2 |
| C2×Q16×D167 | 2 |
| #24923844 | 2 |
| #24923662 | 2 |
| #24923661 | 2 |
| #24923654 | 2 |
| #24923653 | 2 |
| #24923647 | 2 |
| #24923223 | 2 |
| #494×C167 | 2 |
| #3156 | 167 |