Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
162 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #63500 |
| commutator, cosocle | C2×C4×C9 | C23 |
| Frattini | C2×C3×C4 | C22×D3 |
| Fitting | C2×C9×D8 | C2 |
| socle | C2×C3 | #938 |
| hypercenter | C2×D8 | D9 |
| hypocenter | C9 | #472 |
| LCS | G ▷ C2×C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C9×D8 | C2 | semidirect |
| 2. #63495 | C2 | semidirect |
| 3. #63464 | C2 | semidirect |
| 4. #63391 | C2 | semidirect |
| 5. #63372 | C2 | semidirect |
| 55. C2×D8 | D9 | semidirect |
| 93. C9 | #472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D8 | 2 |
| #63495 | 2 |
| #63464 | 2 |
| #63391 | 2 |
| #63372 | 2 |
| #5160 | 3 |