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 |
|---|---|---|
| 32. C32×C8 | Q8 | semidirect |
| 33. C3×C3⋊C8 | Q8 | semidirect |
| 79. C3×C8 | Dic6 | semidirect |
| 80. C3×C8 | Dic6 | semidirect |
| 81. C3⋊C8 | Dic6 | semidirect |
| 110. C32 | #500 | semidirect |
| 118. C8 | #627 | semidirect |
| 136. C3 | #4682 | semidirect |
| 137. C3 | #4874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63918 | 2 |
| #63645 | 2 |
| C3×#818 | 2 |
| C3×C8×Dic3 | 2 |
| #63575 | 2 |
| #4874 | 3 |
| #4682 | 3 |