Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
378 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 125 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. C32×C4⋊C8 | C2 | semidirect |
| 4. #63641 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 19. C3×C4⋊C8 | D3 | semidirect |
| 51. C32×C4 | M16 | semidirect |
| 56. C3⋊Dic3 | M16 | semidirect |
| 61. C4⋊C8 | C3⋊D3 | semidirect |
| 94. C3×C4 | ΓL(1,𝔽25) | semidirect |
| 100. C32 | #423 | semidirect |
| 126. C4 | #3743 | semidirect |
| 129. 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 |
| C42×C3⋊D3 | 2 |
| C32×C4⋊C8 | 2 |
| #63641 | 2 |
| C4⋊(C3⋊(C3⋊C8)) | 2 |
| #4837 | 3 |