Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
242 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 14. #3718 | C4 | direct (N × H) |
| 50. C32×C4 | Q16 | semidirect |
| 98. C3×C4 | #216 | semidirect |
| 103. C32 | C4×Q16 | semidirect |
| 123. C4 | #3718 | direct (N × H) |
| 127. C3 | C4×#216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Dic6 | 2 |
| C2×#3718 | 2 |
| C4×C3⋊(C3⋊C8) | 2 |
| #63576 | 2 |
| #63565 | 2 |
| C4×#216 | 3 |