Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
494 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 76 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×#924 | C2 | semidirect |
| 3. C2×#3717 | C2 | semidirect |
| 4. C3×#830 | C2 | semidirect |
| 5. #63564 | C2 | semidirect |
| 13. C2×C3×Dic6 | C22 | semidirect |
| 15. C3×C4⋊Dic3 | C22 | semidirect |
| 17. C2×C3×C3⋊C8 | C22 | semidirect |
| 24. #924 | D3 | semidirect |
| 27. #830 | D3 | semidirect |
| 62. C2×Dic6 | C2×D3 | semidirect |
| 69. C4⋊Dic3 | C2×D3 | semidirect |
| 71. C2×C3⋊C8 | C2×D3 | semidirect |
| 75. C22×C32 | SD16 | semidirect |
| 155. C22×C3 | #204 | semidirect |
| 156. C22×C3 | #215 | semidirect |
| 181. C32 | #450 | semidirect |
| 218. C22 | #3717 | semidirect |
| 225. C3 | #4731 | semidirect |
| 226. C3 | #5046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊D3) | 2 |
| C3×#924 | 2 |
| C2×#3717 | 2 |
| C3×#830 | 2 |
| #63564 | 2 |
| #5046 | 3 |
| #4731 | 3 |