Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
405 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 405 conjugacy classes of subgroups — too many to draw. Only its 108 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. C2×#3711 | C2 | semidirect |
| 3. #63657 | C2 | semidirect |
| 4. C3×#830 | C2 | semidirect |
| 5. (C2×D3)⋊(C3⋊C8) | C2 | semidirect |
| 16. C2×C3⋊(C3⋊C8) | C22 | semidirect |
| 17. C2×C3×C3⋊C8 | C22 | semidirect |
| 28. #830 | D3 | semidirect |
| 71. C2×C3⋊C8 | C2×D3 | semidirect |
| 75. C22×C32 | M16 | semidirect |
| 83. C2×C3×D3 | M16 | semidirect |
| 166. C22×C3 | ΓL(1,𝔽25) | semidirect |
| 167. C22×C3 | #208 | semidirect |
| 175. C2×D3 | #208 | semidirect |
| 187. C32 | #407 | semidirect |
| 231. C22 | #3711 | semidirect |
| 238. C3 | #4726 | semidirect |
| 239. C3 | #5207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×D3 | 2 |
| C2×#3711 | 2 |
| #63657 | 2 |
| C3×#830 | 2 |
| (C2×D3)⋊(C3⋊C8) | 2 |
| #5207 | 3 |
| #4726 | 3 |