Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
15454 conjugacy classes of subgroups; only the 8408 normal subgroups are shown.
This group has 15454 conjugacy classes of subgroups — too many to draw. Only its 8408 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | #64408 |
| commutator, hypocenter | C73 | C25×C8 |
| Frattini | C2 | C25×#64408 |
| Fitting | C24×C4×C73 | C4 |
| socle | C25×C73 | C2×C4 |
| prime radical | C25×D73 | C4 |
| cosocle | Dic73 | C26 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#11924036 | C2 | direct (N × H) |
| 2. C24×#10596833 | C2 | semidirect |
| 4. C22×#11924036 | C22 | direct (N × H) |
| 5. C23×#10596833 | C22 | semidirect |
| 11. C2×#11924036 | C23 | direct (N × H) |
| 12. C22×#10596833 | C23 | semidirect |
| 13. C24×D73 | C8 | semidirect |
| 21. #11924036 | C24 | direct (N × H) |
| 22. C2×#10596833 | C24 | semidirect |
| 23. C23×D73 | C2×C8 | semidirect |
| 29. C24×C73 | C2×C8 | semidirect |
| 32. C23×C73 | C22×C8 | semidirect |
| 34. C22×D73 | C22×C8 | semidirect |
| 41. #10596833 | C25 | semidirect |
| 42. C22×C73 | C23×C8 | semidirect |
| 44. C2×D73 | C23×C8 | semidirect |
| 50. C2×C73 | C24×C8 | semidirect |
| 52. D73 | C24×C8 | semidirect |
| 56. C73 | C25×C8 | semidirect |
| 76. C24 | #11924036 | direct (N × H) |
| 87. C23 | C2×#11924036 | direct (N × H) |
| 97. C22 | C22×#11924036 | direct (N × H) |
| 103. C2 | C23×#11924036 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11924036 | 2 |
| C24×#10596833 | 2 |
| C24×C4×D73 | 2 |
| C25×C8 | 73 |