Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
714 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×C3⋊D3 |
| commutator, socle, cosocle | C23×C32 | C23 |
| Fitting, prime radical | C22×C32×D4 | C2 |
| hypercenter | C22×D4 | C3⋊D3 |
| hypocenter | C32 | #394 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#3757 | C2 | semidirect |
| 3. C2×#3757 | C2 | semidirect |
| 4. C2×#3750 | C2 | semidirect |
| 5. #63658 | C2 | semidirect |
| 40. C2×C3⋊Dic3 | D4 | semidirect |
| 124. C32 | #394 | semidirect |
| 166. C3 | #5222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D4 | 2 |
| C2×#3757 | 2 |
| C2×#3750 | 2 |
| #63658 | 2 |
| #5222 | 3 |