Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
152 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 34 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×C8×A4 | C2 | semidirect |
| 3. C3×A4⋊C8 | C2 | semidirect |
| 4. #5400 | C3 | direct (N × H) |
| 12. C22×C3×C8 | D3 | semidirect |
| 15. C8×A4 | C2×C3 | semidirect |
| 16. A4⋊C8 | C2×C3 | semidirect |
| 46. C3×A4 | M16 | semidirect |
| 50. C22×C8 | C3×D3 | semidirect |
| 76. C3×C8 | S4 | semidirect |
| 98. C22×C3 | ΓL(1,𝔽25) | semidirect |
| 101. A4 | C3×M16 | semidirect |
| 125. C8 | C3×S4 | semidirect |
| 138. C22 | C3×ΓL(1,𝔽25) | semidirect |
| 146. C3 | #5400 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×S4 | 2 |
| C3×C8×A4 | 2 |
| C3×A4⋊C8 | 2 |
| #5400 | 3 |
| C3×#435 | 3 |
| C3×ΓL(1,𝔽25) | 4 |