Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
1536 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D167 |
| commutator, socle, cosocle | C22×C167 | C25 |
| Fitting | C22×#41×C167 | C2 |
| hypercenter | C22×#41 | D167 |
| hypocenter | C167 | #3487 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C22 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19128880 | C2 | semidirect |
| 2. #24923938 | C2 | semidirect |
| 3. #24923926 | C2 | semidirect |
| 4. #24923836 | C2 | semidirect |
| 5. #24923780 | C2 | semidirect |
| 6. #24923747 | C2 | semidirect |
| 7. C22×#41×C167 | C2 | semidirect |
| 9. C2×#14581951 | C22 | semidirect |
| 11. C2×Q8×D167 | C22 | semidirect |
| 12. #19128828 | C22 | semidirect |
| 13. #19128819 | C22 | semidirect |
| 15. #19128811 | C22 | semidirect |
| 16. #19128806 | C22 | semidirect |
| 17. #19128803 | C22 | semidirect |
| 19. Q8×Dic167 | C22 | semidirect |
| 20. C4×C22⋊D167 | C22 | semidirect |
| 43. C2×Q8×C167 | D4 | semidirect |
| 87. C167 | #3487 | semidirect |
| 90. C22×#41 | D167 | semidirect |
| 121. C2×Q8 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128880 | 2 |
| #24923938 | 2 |
| #24923926 | 2 |
| #24923836 | 2 |
| #24923780 | 2 |
| #24923747 | 2 |
| C22×#41×C167 | 2 |
| #3487 | 167 |