Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
171 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 171 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C9 | C2×D4 |
| commutator | C2×C4 | C23×C9 |
| Frattini, cosocle | C2×C3×C4 | C23×C3 |
| socle | C22×C3 | C2×C3×D4 |
| prime radical | C3×#121 | C2×C3 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C9 ◁ C22×C4×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C9×C4⋊C4 | C2 | semidirect |
| 3. C9×#106 | C2 | semidirect |
| 4. C9×#102 | C2 | semidirect |
| 5. C9×C22⋊C8 | C2 | semidirect |
| 32. #481 | C9 | direct (N × H) |
| 54. C2×C4⋊C4 | C2×C9 | semidirect |
| 55. #106 | C2×C9 | semidirect |
| 56. #102 | C2×C9 | semidirect |
| 57. C22⋊C8 | C2×C9 | semidirect |
| 94. C9 | #481 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#121 | 2 |
| C2×C9×C4⋊C4 | 2 |
| C9×#106 | 2 |
| C9×#102 | 2 |
| C9×C22⋊C8 | 2 |
| C3×#481 | 3 |