Finite Group DatabasebetaFinite Group DatabasebetaOrder 23571.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 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. C3×#14579756 | C3 | semidirect |
| 2. C3×#14579755 | C3 | semidirect |
| 4. C3×C9×C97⋊C3 | C3 | semidirect |
| 5. C32⋊(C97⋊C9) | C3 | semidirect |
| 6. (C3×C97⋊C3)⋊C9 | C3 | semidirect |
| 7. (C3×C97⋊C3)⋊C9 | C3 | semidirect |
| 8. (C3×C97⋊C3)⋊C9 | C3 | semidirect |
| 9. C3×3−1+2×C97 | C3 | semidirect |
| 36. C3×C97⋊C3 | 3−1+2 | semidirect |
| 38. C9×C97 | H(3,𝔽3) | semidirect |
| 50. C97 | C9⋊H(3,𝔽3) | semidirect |
| 53. C3×3−1+2 | C97⋊C3 | semidirect |
| 91. C9 | C32⋊(C97⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14579756 | 3 |
| C3×#14579755 | 3 |
| C3×C32⋊(C97⋊C3) | 3 |
| C3×C9×C97⋊C3 | 3 |
| C32⋊(C97⋊C9) | 3 |
| (C3×C97⋊C3)⋊C9 | 3 |
| C3×3−1+2×C97 | 3 |
| C9⋊H(3,𝔽3) | 97 |