Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
238 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 3. #63578 | C2 | semidirect |
| 85. C32 | #430 | semidirect |
| 107. C3 | #5124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3748 | 2 |
| C2×C3×#208 | 2 |
| #63578 | 2 |
| #5124 | 3 |