Finite Group DatabasebetaFinite Group DatabasebetaOrder 5184.
1838 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 1838 conjugacy classes of subgroups — too many to draw. Only its 184 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×#63692⋊C3 | C2 | semidirect |
| 2. C3×#63691⋊C3 | C2 | semidirect |
| 3. C3×#11722576 | C2 | semidirect |
| 5. #13164434 | C3 | direct (N × H) |
| 6. C3×#10593100 | C3 | semidirect |
| 8. C3×#88691 | C22 | semidirect |
| 9. C3×#3689⋊C3 | C22 | semidirect |
| 10. C3×#3688⋊C3 | C22 | semidirect |
| 19. #11722576 | C2×C3 | semidirect |
| 21. C3×#63700 | C2×C3 | semidirect |
| 22. C3×#63692 | C2×C3 | semidirect |
| 23. C3×#63691 | C2×C3 | semidirect |
| 24. #63692⋊C3 | C2×C3 | semidirect |
| 25. #63691⋊C3 | C2×C3 | semidirect |
| 33. #10593100 | C32 | semidirect |
| 51. #88691 | C22×C3 | semidirect |
| 53. C3×#41⋊C9 | C22×C3 | semidirect |
| 54. C3×#3689 | C22×C3 | semidirect |
| 55. #3689⋊C3 | C22×C3 | semidirect |
| 56. C3×#3688 | C22×C3 | semidirect |
| 57. #3688⋊C3 | C22×C3 | semidirect |
| 85. #63700 | C2×C32 | semidirect |
| 86. #63692 | C2×C32 | semidirect |
| 87. #63691 | C2×C32 | semidirect |
| 169. #41⋊C9 | C22×C32 | semidirect |
| 170. #3689 | C22×C32 | semidirect |
| 171. #3688 | C22×C32 | semidirect |
| 191. C3×H(5,𝔽2) | AGL(1,ℤ/9) | semidirect |
| 359. H(5,𝔽2) | C3×AGL(1,ℤ/9) | semidirect |
| 520. C3 | #13164434 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63692⋊C3 | 2 |
| C3×#63691⋊C3 | 2 |
| C3×#11722576 | 2 |
| C32×#5835 | 3 |
| #13164434 | 3 |
| C3×#10593100 | 3 |
| C3×#88724 | 4 |