Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
714 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C32×C22⋊C4 | C2 | semidirect |
| 3. C2×#3757 | C2 | semidirect |
| 4. C2×#3752 | C2 | semidirect |
| 5. C2×#3752 | C2 | semidirect |
| 6. C2×#3750 | C2 | semidirect |
| 7. #63658 | C2 | semidirect |
| 25. C2×C3×C22⋊C4 | D3 | semidirect |
| 61. C2×C3⋊Dic3 | D4 | semidirect |
| 109. C2×C22⋊C4 | C3⋊D3 | semidirect |
| 192. C32 | #394 | semidirect |
| 259. C3 | #4959 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#638 | 2 |
| C2×C32×C22⋊C4 | 2 |
| C2×#3757 | 2 |
| C2×#3752 | 2 |
| C2×#3750 | 2 |
| #63658 | 2 |
| #4959 | 3 |