Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
398 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 80 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×#3712 | C2 | semidirect |
| 3. C2×#3710 | C2 | semidirect |
| 4. C3×#830 | C2 | semidirect |
| 5. #63557 | C2 | semidirect |
| 25. #830 | D3 | semidirect |
| 172. C32 | #408 | semidirect |
| 216. C3 | #4727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3828 | 2 |
| C2×#3712 | 2 |
| C2×#3710 | 2 |
| C3×#830 | 2 |
| #63557 | 2 |
| #4727 | 3 |