Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
274 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 114 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×Q8×Dic3 | C2 | semidirect |
| 4. C3×#835 | C2 | semidirect |
| 6. C3×#818 | C2 | semidirect |
| 7. C3×#815 | C2 | semidirect |
| 9. #5164 | C3 | direct (N × H) |
| 13. C32×SD16 | C4 | semidirect |
| 27. Q8×Dic3 | C2×C3 | semidirect |
| 33. #835 | C2×C3 | semidirect |
| 35. #818 | C2×C3 | semidirect |
| 36. #815 | C2×C3 | semidirect |
| 39. C32×Q8 | C2×C4 | semidirect |
| 49. C32×C8 | C2×C4 | semidirect |
| 61. C3×SD16 | Dic3 | semidirect |
| 62. C3×SD16 | C3×C4 | semidirect |
| 105. C3×Q8 | C2×Dic3 | semidirect |
| 106. C3×Q8 | C2×C3×C4 | semidirect |
| 131. C3×C8 | C2×Dic3 | semidirect |
| 132. C3×C8 | C2×C3×C4 | semidirect |
| 141. SD16 | C3×Dic3 | semidirect |
| 179. C32 | #440 | semidirect |
| 182. Q8 | C2×C3×Dic3 | semidirect |
| 193. C8 | C2×C3×Dic3 | semidirect |
| 218. C3 | #5164 | direct (N × H) |
| 219. C3 | C3×#440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×SD16 | 2 |
| C3×Q8×Dic3 | 2 |
| C3×D4×Dic3 | 2 |
| C3×#835 | 2 |
| C3×#832 | 2 |
| C3×#818 | 2 |
| C3×#815 | 2 |
| C3×#440 | 3 |
| #5164 | 3 |