Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
486 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 191 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. C2×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 3. C2×#3748 | C2 | semidirect |
| 4. #63662 | C2 | semidirect |
| 5. #63659 | C2 | semidirect |
| 8. C32×#41 | C4 | semidirect |
| 27. C32×Q8 | C2×C4 | semidirect |
| 30. C32×D4 | C2×C4 | semidirect |
| 42. C3×#41 | Dic3 | semidirect |
| 73. C3×Q8 | C2×Dic3 | semidirect |
| 76. C3×D4 | C2×Dic3 | semidirect |
| 92. #41 | C3⋊Dic3 | semidirect |
| 115. C32 | #417 | semidirect |
| 119. Q8 | C2×C3⋊Dic3 | semidirect |
| 122. D4 | C2×C3⋊Dic3 | semidirect |
| 149. C3 | #5232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#41 | 2 |
| C2×C4⋊(C3⋊Dic3) | 2 |
| C2×#3748 | 2 |
| #63662 | 2 |
| #63659 | 2 |
| #5232 | 3 |