Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
306 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. C3×C4⋊(C3⋊C8) | C2 | semidirect |
| 4. #63572 | C2 | semidirect |
| 20. C4⋊(C3⋊C8) | D3 | semidirect |
| 56. C32×C4 | M16 | semidirect |
| 61. C3⋊Dic3 | M16 | semidirect |
| 116. C3×C4 | ΓL(1,𝔽25) | semidirect |
| 125. C32 | #423 | semidirect |
| 154. C4 | #3712 | semidirect |
| 158. C3 | #4837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C3⋊D3 | 2 |
| C2×#3712 | 2 |
| C3×C4⋊(C3⋊C8) | 2 |
| #63572 | 2 |
| #4837 | 3 |