Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
438 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 84 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. C22×#622 | C2 | semidirect |
| 3. C22⋊#622 | C2 | direct (N × H) |
| 11. C2×#622 | C22 | semidirect |
| 15. C23×C32 | C8 | semidirect |
| 38. C22×C32 | C2×C8 | semidirect |
| 60. C2×C32 | C22⋊C8 | semidirect |
| 83. C32 | C2×C22⋊C8 | semidirect |
| 86. C23 | #622 | semidirect |
| 106. C22 | C2×#622 | semidirect |
| 115. C2 | C22⋊#622 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊Dic3 | 2 |
| C22×#622 | 2 |
| C22⋊#622 | 2 |
| C2×C22⋊C8 | 9 |