Finite Group DatabasebetaFinite Group DatabasebetaOrder 23571.
120 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C97⋊C3 |
| commutator, socle, cosocle | C32×C97 | C33 |
| Fitting | C9⋊C9×C97 | C3 |
| prime radical | C32×C97⋊C3 | C32 |
| hypercenter | C9⋊C9 | C97⋊C3 |
| hypocenter | C97 | #6896 |
| LCS | G ▷ C32×C97 ▷ C97 | |
| UCS | C1 ◁ C32 ◁ C9⋊C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. (C97⋊C9)⋊C9 | C3 | semidirect |
| 4. (C97⋊C9)⋊C9 | C3 | semidirect |
| 5. (C97⋊C9)⋊C9 | C3 | semidirect |
| 6. (C97⋊C9)⋊C9 | C3 | semidirect |
| 7. (C97⋊C9)⋊C9 | C3 | semidirect |
| 8. (C97⋊C9)⋊C9 | C3 | semidirect |
| 9. (C97⋊C9)⋊C9 | C3 | semidirect |
| 12. C9×C97⋊C9 | C3 | semidirect |
| 13. C9⋊C9×C97 | C3 | semidirect |
| 44. C97⋊C9 | 3−1+2 | semidirect |
| 45. C97⋊C9 | 3−1+2 | semidirect |
| 52. C97 | #6896 | semidirect |
| 62. C9⋊C9 | 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 |
| (C97⋊C9)⋊C9 | 3 |
| (C3×C97⋊C3)⋊C9 | 3 |
| C9×C97⋊C9 | 3 |
| C9⋊C9×C97 | 3 |
| #6896 | 97 |