Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
318 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 4. #63784 | C2 | direct (N × H) |
| 6. C2×C32×Q8 | C4 | semidirect |
| 9. Q8×C3⋊D3 | C4 | semidirect |
| 14. C2×#634 | C4 | semidirect |
| 25. C32×Q8 | C2×C4 | semidirect |
| 39. #634 | C2×C4 | semidirect |
| 84. C2×C32 | #103 | semidirect |
| 86. C3⋊D3 | #103 | semidirect |
| 95. C2×Q8 | #157 | semidirect |
| 115. C32 | C2×#103 | semidirect |
| 122. Q8 | C2×#157 | semidirect |
| 157. C2 | #63784 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C3⋊D3 | 2 |
| C2×C4⋊#157 | 2 |
| C2×#3787 | 2 |
| #63784 | 2 |
| C2×#103 | 9 |