Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
372 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 372 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. C22×C32×C8 | C2 | semidirect |
| 3. C2×#3743 | C2 | semidirect |
| 4. #63657 | C2 | semidirect |
| 5. #63647 | C2 | semidirect |
| 6. #63642 | C2 | semidirect |
| 7. #63641 | C2 | semidirect |
| 22. C22×C3×C8 | D3 | semidirect |
| 42. C32×C8 | D4 | semidirect |
| 61. C22×C32 | M16 | semidirect |
| 73. C22×C8 | C3⋊D3 | semidirect |
| 92. C3×C8 | #67 | semidirect |
| 115. C22×C3 | ΓL(1,𝔽25) | semidirect |
| 126. C32 | #435 | semidirect |
| 142. C8 | #638 | semidirect |
| 153. C22 | #3743 | semidirect |
| 161. C3 | #5111 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C8 | 2 |
| C4×#638 | 2 |
| C2×#3743 | 2 |
| #63657 | 2 |
| #63647 | 2 |
| #63642 | 2 |
| #63641 | 2 |
| #5111 | 3 |