Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
127 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 127 conjugacy classes of subgroups — too many to draw. Only its 24 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. C2×#3688 | C2 | semidirect |
| 3. #63421 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41⋊C9 | 2 |
| C2×#3688 | 2 |
| #63421 | 2 |
| #5239 | 3 |
| Dic9⋊C4 | 4 |