Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
498 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 4. #63919 | C2 | semidirect |
| 5. C4×#627 | C2 | semidirect |
| 6. #63872 | C2 | semidirect |
| 28. C2×C32×C4 | Q8 | semidirect |
| 77. C2×C3×C4 | Dic6 | semidirect |
| 118. C32 | #533 | semidirect |
| 125. C2×C4 | #627 | semidirect |
| 143. C3 | #5517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊Dic3 | 2 |
| C3×#926 | 2 |
| #63982 | 2 |
| #63919 | 2 |
| C4×#627 | 2 |
| #63872 | 2 |
| #5517 | 3 |