Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1800 conjugacy classes of subgroups; only the 776 normal subgroups are shown.
This group has 1800 conjugacy classes of subgroups — too many to draw. Only its 776 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×#64408 |
| commutator, socle | C22×C73 | C24×C4 |
| Fitting | #564×C73 | C4 |
| prime radical, cosocle | C22×D73 | C25 |
| hypercenter | #564 | #64408 |
| hypocenter | C73 | C4×#564 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #564 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C73⋊#564 | C4 | semidirect |
| 11. #564×C73 | C4 | semidirect |
| 45. #64408 | #564 | direct (N × H) |
| 55. C73 | C4×#564 | semidirect |
| 57. #564 | #64408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626477 | 2 |
| #125×#64408 | 2 |
| #564×D73 | 2 |
| C4×#564 | 73 |