Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
186 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 87 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 | C2×C3×D4 | C22×C3 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C9 ◁ C42×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C9×Q16 | C2 | semidirect |
| 3. C9×C4⋊Q8 | C2 | semidirect |
| 5. C9×#97 | C2 | semidirect |
| 31. #497 | C9 | direct (N × H) |
| 48. C2×Q16 | C2×C9 | semidirect |
| 50. C4⋊Q8 | C2×C9 | semidirect |
| 52. #97 | C2×C9 | semidirect |
| 82. C9 | #497 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×Q16 | 2 |
| C2×C9×SD16 | 2 |
| C9×C4⋊Q8 | 2 |
| C9×#124 | 2 |
| C9×#97 | 2 |
| C3×#497 | 3 |