Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
255 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C9 | C23 |
| commutator | C23 | C23×C9 |
| Frattini, socle, cosocle | C23×C3 | C23×C3 |
| prime radical | C24×C3 | C22×C3 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C9×C4⋊C4 | C2 | semidirect |
| 4. C9×#95 | C2 | semidirect |
| 5. C9×#95 | C2 | semidirect |
| 36. #397 | C9 | direct (N × H) |
| 59. C2×C4⋊C4 | C2×C9 | semidirect |
| 62. #95 | C2×C9 | semidirect |
| 63. #95 | C2×C9 | semidirect |
| 108. C9 | #397 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×C4⋊C4 | 2 |
| C2×C9×C22⋊C4 | 2 |
| C9×#95 | 2 |
| C3×#397 | 3 |