Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
870 conjugacy classes of subgroups; only the 295 normal subgroups are shown.
This group has 870 conjugacy classes of subgroups — too many to draw. Only its 295 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 |
|---|---|---|
| 3. #64153 | C2 | direct (N × H) |
| 29. C2×C3⋊Dic3 | Q8 | semidirect |
| 50. C3⋊Dic3 | C2×Q8 | semidirect |
| 67. C2×C32 | C4⋊Q8 | semidirect |
| 87. C32 | C2×C4⋊Q8 | semidirect |
| 99. C2×C3 | #944 | semidirect |
| 109. C3 | C2×#944 | semidirect |
| 110. C2 | #64153 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q8 | 2 |
| C22×#634 | 2 |
| #64153 | 2 |
| C2×#3750 | 2 |
| C2×C4×C3⋊Dic3 | 2 |
| C2×#944 | 3 |