Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
246 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 83 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×#3746 | C2 | semidirect |
| 3. #63656 | C2 | semidirect |
| 4. #63654 | C2 | semidirect |
| 5. #63639 | C2 | semidirect |
| 80. C32 | #510 | semidirect |
| 100. C3 | #5195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#135 | 2 |
| C2×#3746 | 2 |
| #63656 | 2 |
| #63654 | 2 |
| #63639 | 2 |
| #5195 | 3 |