Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
1531 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 1531 conjugacy classes of subgroups — too many to draw. Only its 290 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D92 |
| commutator, hypocenter | C92 | C23×C4 |
| Frattini | C2×C32 | C22×D32 |
| Fitting | C23×C92 | C22 |
| socle | C23×C32 | D32 |
| prime radical | C23×C9⋊D9 | C2 |
| cosocle | C2×C92 | C24 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C9×Dic9 | C2 | semidirect |
| 3. C2×#10619528 | C2 | direct (N × H) |
| 6. C22×C9⋊D9 | C4 | semidirect |
| 8. C2×C9×Dic9 | C22 | semidirect |
| 9. #10619528 | C22 | direct (N × H) |
| 15. C22×C92 | C2×C4 | semidirect |
| 17. C2×C9⋊D9 | C2×C4 | semidirect |
| 19. C9×Dic9 | C23 | semidirect |
| 31. C2×C92 | C22×C4 | semidirect |
| 33. C9⋊D9 | C22×C4 | semidirect |
| 41. C22×Dic9 | D9 | semidirect |
| 54. C92 | C23×C4 | semidirect |
| 70. C2×Dic9 | C2×D9 | semidirect |
| 92. C22×C9 | C4×D9 | semidirect |
| 101. Dic9 | C22×D9 | semidirect |
| 121. C2×C9 | C2×C4×D9 | semidirect |
| 142. C9 | C22×C4×D9 | semidirect |
| 156. C22 | #10619528 | direct (N × H) |
| 162. C2 | C2×#10619528 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C9⋊D9 | 2 |
| C22×C9×Dic9 | 2 |
| C2×#10619528 | 2 |
| C22×(C3⋊D9)⋊C4 | 3 |