Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C22×C3⋊(C3⋊C8) | C2 | semidirect |
| 3. C2×#3743 | C2 | semidirect |
| 4. C32×C22⋊C8 | C2 | semidirect |
| 5. #63647 | C2 | semidirect |
| 6. #63642 | C2 | semidirect |
| 7. #63641 | C2 | semidirect |
| 25. C3×C22⋊C8 | D3 | semidirect |
| 44. C3⋊(C3⋊C8) | D4 | semidirect |
| 61. C22×C32 | M16 | semidirect |
| 77. C22⋊C8 | C3⋊D3 | semidirect |
| 115. C22×C3 | ΓL(1,𝔽25) | semidirect |
| 126. C32 | #435 | semidirect |
| 153. C22 | #3743 | semidirect |
| 161. C3 | #4730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#638 | 2 |
| C22×C3⋊(C3⋊C8) | 2 |
| C2×#3743 | 2 |
| C32×C22⋊C8 | 2 |
| #63647 | 2 |
| #63642 | 2 |
| #63641 | 2 |
| #4730 | 3 |