Finite Group DatabasebetaFinite Group DatabasebetaOrder 19197.
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×C79⋊C3 |
| commutator, socle, cosocle | C32×C79 | C33 |
| Fitting | C79×C9⋊C9 | C3 |
| prime radical | C32×C79⋊C3 | C32 |
| hypercenter | C9⋊C9 | C79⋊C3 |
| hypocenter | C79 | #6896 |
| LCS | G ▷ C32×C79 ▷ C79 | |
| UCS | C1 ◁ C32 ◁ C9⋊C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. (C79⋊C9)⋊C9 | C3 | semidirect |
| 4. (C79⋊C9)⋊C9 | C3 | semidirect |
| 5. (C79⋊C9)⋊C9 | C3 | semidirect |
| 6. (C79⋊C9)⋊C9 | C3 | semidirect |
| 7. (C79⋊C9)⋊C9 | C3 | semidirect |
| 8. (C79⋊C9)⋊C9 | C3 | semidirect |
| 9. (C79⋊C9)⋊C9 | C3 | semidirect |
| 12. C9×C79⋊C9 | C3 | semidirect |
| 13. C79×C9⋊C9 | C3 | semidirect |
| 44. C79⋊C9 | 3−1+2 | semidirect |
| 45. C79⋊C9 | 3−1+2 | semidirect |
| 61. C9⋊C9 | C79⋊C3 | semidirect |
| 65. C79 | #6896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14523839 | 3 |
| C3×#14523838 | 3 |
| (C79⋊C9)⋊C9 | 3 |
| (C3×C79⋊C3)⋊C9 | 3 |
| C9×C79⋊C9 | 3 |
| C79×C9⋊C9 | 3 |
| #6896 | 79 |