Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
239 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 5. Q8×C3⋊C8 | C3 | direct (N × H) |
| 18. C32×Q8 | C8 | semidirect |
| 23. C3×C3⋊C8 | Q8 | direct (N × H) |
| 47. C3×Q8 | C3⋊C8 | direct (N × H) |
| 48. C3×Q8 | C3×C8 | semidirect |
| 61. C3⋊C8 | C3×Q8 | direct (N × H) |
| 85. C32 | C8×Q8 | semidirect |
| 86. Q8 | C3×C3⋊C8 | direct (N × H) |
| 107. C3 | Q8×C3⋊C8 | direct (N × H) |
| 108. C3 | C3×C8×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×Q8 | 2 |
| C3×C4⋊(C3⋊C8) | 2 |
| C3×C4×C3⋊C8 | 2 |
| C3×C8×Q8 | 3 |
| Q8×C3⋊C8 | 3 |