Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
214 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 31. C32×C8 | Q8 | semidirect |
| 32. C3×C3⋊C8 | Q8 | semidirect |
| 75. C3×C8 | Dic6 | semidirect |
| 76. C3×C8 | Dic6 | semidirect |
| 77. C3⋊C8 | Dic6 | semidirect |
| 103. C32 | #498 | semidirect |
| 110. C8 | #627 | semidirect |
| 124. C3 | #4680 | semidirect |
| 125. C3 | #4855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63918 | 2 |
| #63644 | 2 |
| C3×#817 | 2 |
| C3×C8×Dic3 | 2 |
| #63573 | 2 |
| #4855 | 3 |
| #4680 | 3 |