Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2046 conjugacy classes of subgroups; only the 1152 normal subgroups are shown.
This group has 2046 conjugacy classes of subgroups — too many to draw. Only its 1152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | #64408 |
| commutator, hypocenter | C73 | C2×C42×C8 |
| Frattini | C23 | C23×#64408 |
| Fitting | C43×C73 | C4 |
| socle | C23×C73 | C23×C4 |
| prime radical | C23×D73 | C22×C4 |
| cosocle | C22×Dic73 | C24 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C42×#10596833 | C2 | semidirect |
| 5. C4×#11924036 | C4 | direct (N × H) |
| 14. C4×#10596833 | C2×C4 | semidirect |
| 20. C42×D73 | C8 | semidirect |
| 24. #11924036 | C42 | direct (N × H) |
| 33. C4×Dic73 | C2×C8 | semidirect |
| 38. C42×C73 | C2×C8 | semidirect |
| 48. C4×D73 | C4×C8 | semidirect |
| 50. #10596833 | C2×C42 | semidirect |
| 56. C4×C73 | C2×C4×C8 | semidirect |
| 57. Dic73 | C2×C4×C8 | semidirect |
| 62. D73 | C42×C8 | semidirect |
| 66. C73 | C2×C42×C8 | semidirect |
| 101. C42 | #11924036 | direct (N × H) |
| 121. C4 | C4×#11924036 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11924036 | 2 |
| C42×#10596833 | 2 |
| C43×D73 | 2 |
| C2×C42×C8 | 73 |