Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
2714 conjugacy classes of subgroups; only the 672 normal subgroups are shown.
This group has 2714 conjugacy classes of subgroups — too many to draw. Only its 672 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×C9⋊D9 |
| commutator, cosocle | C2×C92 | C24 |
| Frattini | C2×C32 | C23×C3⋊D3 |
| Fitting | C24×C92 | C2 |
| socle | C23×C32 | C2×C3⋊D3 |
| hypercenter | C24 | C9⋊D9 |
| hypocenter | C92 | C22×D4 |
| LCS | G ▷ C2×C92 ▷ C92 | |
| UCS | C1 ◁ C23 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×C92 | C2 | semidirect |
| 2. C23×C9⋊D9 | C2 | semidirect |
| 3. C2×#10619673 | C2 | direct (N × H) |
| 4. C22×C9⋊Dic9 | C2 | semidirect |
| 8. C23×C92 | C22 | semidirect |
| 10. C22×C9⋊D9 | C22 | semidirect |
| 11. #10619673 | C22 | direct (N × H) |
| 12. C2×C9⋊Dic9 | C22 | semidirect |
| 18. C22×C92 | D4 | semidirect |
| 20. C22×C92 | C23 | semidirect |
| 22. C2×C9⋊D9 | C23 | semidirect |
| 23. C9⋊Dic9 | C23 | semidirect |
| 34. C2×C92 | C2×D4 | semidirect |
| 41. C24×C9 | D9 | semidirect |
| 53. C92 | C22×D4 | semidirect |
| 63. C23×C9 | C2×D9 | semidirect |
| 84. C22×C9 | #611 | semidirect |
| 86. C22×C9 | C22×D9 | semidirect |
| 104. C2×C9 | C2×#611 | semidirect |
| 108. C24 | C9⋊D9 | semidirect |
| 119. C9 | C22×#611 | semidirect |
| 124. C23 | C2×C9⋊D9 | semidirect |
| 134. C22 | #10619673 | direct (N × H) |
| 136. C22 | C22×C9⋊D9 | semidirect |
| 141. C2 | C2×#10619673 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C92 | 2 |
| C23×C9⋊D9 | 2 |
| C2×#10619673 | 2 |
| C22×C9⋊Dic9 | 2 |
| C22×#6233 | 3 |