Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
231 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C9 | C2×D4 |
| commutator | C4 | C22×C4×C9 |
| Frattini, cosocle | C2×C3×C4 | C23×C3 |
| socle | C2×C3 | C2×C3×C22⋊C4 |
| prime radical | C2×C3×#41 | C2×C3 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C9 ◁ C22×C4×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C9×M16 | C2 | semidirect |
| 3. C9×#117 | C2 | semidirect |
| 4. C9×#104 | C2 | semidirect |
| 8. C9×#41 | C4 | semidirect |
| 10. C2×Q8×C9 | C4 | semidirect |
| 12. C2×D4×C9 | C4 | semidirect |
| 16. C9×M16 | C22 | semidirect |
| 20. C42×C9 | C22 | semidirect |
| 44. #421 | C9 | direct (N × H) |
| 73. C2×M16 | C2×C9 | semidirect |
| 74. #117 | C2×C9 | semidirect |
| 75. #104 | C2×C9 | semidirect |
| 102. #41 | C4×C9 | semidirect |
| 104. C2×Q8 | C4×C9 | semidirect |
| 106. C2×D4 | C4×C9 | semidirect |
| 110. M16 | C22×C9 | semidirect |
| 114. C42 | C22×C9 | semidirect |
| 127. C9 | #421 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#41 | 2 |
| C2×C9×M16 | 2 |
| C9×#117 | 2 |
| C9×#104 | 2 |
| C3×#421 | 3 |