Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
286 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 286 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 |
|---|---|---|
| 4. C3×Dic3⋊C8 | C2 | semidirect |
| 5. Dic3⋊(C3⋊C8) | C2 | semidirect |
| 23. Dic3⋊C8 | D3 | semidirect |
| 61. C3×Dic3 | M16 | semidirect |
| 118. Dic3 | ΓL(1,𝔽25) | semidirect |
| 119. C32 | #423 | semidirect |
| 147. C3 | #4837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3743 | 2 |
| C4×#624 | 2 |
| C2×#3712 | 2 |
| C3×Dic3⋊C8 | 2 |
| Dic3⋊(C3⋊C8) | 2 |
| #4837 | 3 |