Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
266 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 4. #63572 | C2 | semidirect |
| 118. C32 | #424 | semidirect |
| 144. C3 | #5102 | semidirect |
| 145. C3 | #5119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64135 | 2 |
| C2×C3×#208 | 2 |
| C22×C3×C3⋊C8 | 2 |
| #63572 | 2 |
| #5119 | 3 |
| #5102 | 3 |