Finite Group DatabasebetaFinite Group DatabasebetaOrder 21568.
240 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 240 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 | #121×C337 | C2 |
| hypercenter | #121 | D337 |
| hypocenter | C337 | #540 |
| LCS | G ▷ C22×C337 ▷ C337 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #24924955 | C2 | semidirect |
| 2. #24924950 | C2 | semidirect |
| 3. #24924943 | C2 | semidirect |
| 4. #24924941 | C2 | semidirect |
| 5. #24924933 | C2 | semidirect |
| 6. #24924931 | C2 | semidirect |
| 7. #24924930 | C2 | semidirect |
| 8. D4×Dic337 | C2 | semidirect |
| 9. #24924921 | C2 | semidirect |
| 10. #24924918 | C2 | semidirect |
| 11. #121×C337 | C2 | semidirect |
| 79. C337 | #540 | semidirect |
| 88. #121 | D337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924955 | 2 |
| #24924950 | 2 |
| #24924943 | 2 |
| #24924941 | 2 |
| #24924933 | 2 |
| #24924931 | 2 |
| #24924930 | 2 |
| D4×Dic337 | 2 |
| #24924921 | 2 |
| #24924918 | 2 |
| #121×C337 | 2 |
| #540 | 337 |