Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
398 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 96 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. C3×#926 | C2 | semidirect |
| 3. #63581 | C2 | semidirect |
| 9. C2×C4⋊(C3⋊D3) | C4 | semidirect |
| 10. C2×C4×C3⋊D3 | C4 | semidirect |
| 11. C2×#634 | C4 | semidirect |
| 18. #926 | D3 | semidirect |
| 136. C32 | #410 | semidirect |
| 170. C3 | #5006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3828 | 2 |
| C3×#926 | 2 |
| #63581 | 2 |
| #5006 | 3 |