Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
357 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 357 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D9 |
| commutator, cosocle | C23×C9 | C23 |
| Frattini, socle | C23×C3 | C22×D3 |
| Fitting | C22×D4×C9 | C2 |
| prime radical | C22×C3×D4 | D3 |
| hypercenter | C22×D4 | D9 |
| hypocenter | C9 | #394 |
| LCS | G ▷ C23×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#3676 | C2 | semidirect |
| 3. C2×#3676 | C2 | semidirect |
| 4. C2×Dic9⋊C4 | C2 | semidirect |
| 5. C9⋊#95 | C2 | semidirect |
| 40. C2×Dic9 | D4 | semidirect |
| 124. C9 | #394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C9 | 2 |
| C2×#3676 | 2 |
| C2×Dic9⋊C4 | 2 |
| C9⋊#95 | 2 |
| #5222 | 3 |