Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
570 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 192 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×C8×C3⋊D3 | C2 | semidirect |
| 3. C2×C3×ΓL(1,𝔽25) | C2 | semidirect |
| 4. C2×#3712 | C2 | semidirect |
| 5. C2×D3×C3⋊C8 | C2 | semidirect |
| 6. #63805 | C2 | direct (N × H) |
| 17. C8×C3⋊D3 | C22 | semidirect |
| 19. C3×ΓL(1,𝔽25) | C22 | semidirect |
| 20. #3712 | C22 | semidirect |
| 21. D3×C3⋊C8 | C22 | semidirect |
| 27. C2×ΓL(1,𝔽25) | D3 | semidirect |
| 66. ΓL(1,𝔽25) | C2×D3 | semidirect |
| 113. C2×C32 | #131 | semidirect |
| 149. C32 | C2×#131 | semidirect |
| 168. C2×C3 | #907 | semidirect |
| 183. C3 | C2×#907 | semidirect |
| 186. C2 | #63805 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3798 | 2 |
| C2×C8×C3⋊D3 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| C2×#3712 | 2 |
| C2×D3×C3⋊C8 | 2 |
| #63805 | 2 |
| C2×#907 | 3 |