Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
211 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 211 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 |
|---|---|---|
| 1. C22×C3×SL(2,𝔽3) | C2 | semidirect |
| 2. C2×C3×GL(2,𝔽3) | C2 | semidirect |
| 3. C3×#859 | C2 | semidirect |
| 4. #5421 | C3 | direct (N × H) |
| 10. C22×C3×Q8 | D3 | semidirect |
| 12. C22×SL(2,𝔽3) | C2×C3 | semidirect |
| 13. C2×GL(2,𝔽3) | C2×C3 | semidirect |
| 17. #859 | C2×C3 | semidirect |
| 25. C3×SL(2,𝔽3) | D4 | semidirect |
| 55. C22×Q8 | C3×D3 | semidirect |
| 70. C3×Q8 | #67 | semidirect |
| 82. SL(2,𝔽3) | C3×D4 | semidirect |
| 117. C22×C3 | GL(2,𝔽3) | semidirect |
| 133. Q8 | C3×#67 | semidirect |
| 163. C22 | C3×GL(2,𝔽3) | semidirect |
| 171. C3 | #5421 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×SL(2,𝔽3) | 2 |
| C2×C3×GL(2,𝔽3) | 2 |
| C3×#859 | 2 |
| #5421 | 3 |
| C3×#448 | 3 |
| C2×C3×#67 | 4 |