Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
366 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. C2×#3743 | C2 | semidirect |
| 3. C32×C4×C8 | C2 | semidirect |
| 4. #63647 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 18. C3×C4×C8 | D3 | semidirect |
| 30. C32×C8 | D4 | semidirect |
| 47. C32×C4 | M16 | semidirect |
| 55. C4×C8 | C3⋊D3 | semidirect |
| 65. C3×C8 | D12 | semidirect |
| 85. C3×C4 | ΓL(1,𝔽25) | semidirect |
| 89. C32 | #436 | semidirect |
| 100. C8 | C4⋊(C3⋊D3) | semidirect |
| 111. C4 | #3743 | semidirect |
| 114. C3 | #4688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3743 | 2 |
| C4×C4⋊(C3⋊D3) | 2 |
| C32×C4×C8 | 2 |
| #63647 | 2 |
| C4⋊(C3⋊(C3⋊C8)) | 2 |
| #4688 | 3 |