Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
287 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 287 conjugacy classes of subgroups — too many to draw. Only its 74 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×#869 | C2 | semidirect |
| 4. C3×C4⋊(C3⋊C8) | C2 | semidirect |
| 5. #63566 | C2 | semidirect |
| 24. #869 | D3 | semidirect |
| 28. C4⋊(C3⋊C8) | D3 | semidirect |
| 72. C32×C4 | SD16 | semidirect |
| 147. C3×C4 | #204 | semidirect |
| 148. C3×C4 | #215 | semidirect |
| 157. C32 | #461 | semidirect |
| 189. C4 | #3717 | semidirect |
| 193. C3 | #4841 | semidirect |
| 194. C3 | #5083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊D3) | 2 |
| C3×#869 | 2 |
| C2×#3717 | 2 |
| C3×C4⋊(C3⋊C8) | 2 |
| #63566 | 2 |
| #5083 | 3 |
| #4841 | 3 |