Finite Group DatabasebetaFinite Group DatabasebetaOrder 21568.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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 | C23×D337 |
| commutator, socle, cosocle | C22×C337 | C24 |
| Fitting | #123×C337 | C2 |
| prime radical | #24924931 | C2 |
| hypercenter | #123 | D337 |
| hypocenter | C337 | #539 |
| LCS | G ▷ C22×C337 ▷ C337 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #24924954 | C2 | semidirect |
| 2. #24924952 | C2 | semidirect |
| 3. #24924950 | C2 | semidirect |
| 4. #24924949 | C2 | semidirect |
| 5. #24924943 | C2 | semidirect |
| 6. #24924942 | C2 | semidirect |
| 7. #24924941 | C2 | semidirect |
| 8. #24924939 | C2 | semidirect |
| 9. #24924936 | C2 | semidirect |
| 10. #24924936 | C2 | semidirect |
| 12. D4×Dic337 | C2 | semidirect |
| 13. #24924919 | C2 | semidirect |
| 14. C2×C4⋊Dic337 | C2 | semidirect |
| 15. #123×C337 | C2 | semidirect |
| 103. C337 | #539 | semidirect |
| 112. #123 | D337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924954 | 2 |
| #24924952 | 2 |
| #24924950 | 2 |
| #24924949 | 2 |
| #24924943 | 2 |
| #24924942 | 2 |
| #24924941 | 2 |
| #24924939 | 2 |
| #24924936 | 2 |
| #24924931 | 2 |
| D4×Dic337 | 2 |
| #24924919 | 2 |
| C2×C4⋊Dic337 | 2 |
| #123×C337 | 2 |
| #539 | 337 |