Finite Group DatabasebetaFinite Group DatabasebetaOrder 29988.
152 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | #64418⋊C2 |
| commutator, cosocle, hypocenter | #3862 | C22×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C17 | C2×D3 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C3×C17 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C17×#64418 | C2 | semidirect |
| 2. C3×C17×#64425 | C2 | semidirect |
| 4. C17×#64418⋊C2 | C3 | direct (N × H) |
| 5. C3×C17×#3862 | C22 | semidirect |
| 6. C3×C17×C7⋊D7 | D3 | semidirect |
| 8. C17×#64418 | C2×C3 | semidirect |
| 10. C17×#64425 | C2×C3 | semidirect |
| 13. C17×#3862 | C22×C3 | semidirect |
| 14. C3×C72×C17 | C2×D3 | semidirect |
| 16. C3×#64418⋊C2 | C17 | direct (N × H) |
| 17. C17×C7⋊D7 | C3×D3 | semidirect |
| 21. C3×#64425 | C2×C17 | semidirect |
| 22. C3×#64418 | C2×C17 | semidirect |
| 23. C72×C17 | C2×C3×D3 | semidirect |
| 32. #64418⋊C2 | C3×C17 | direct (N × H) |
| 34. C3×#3862 | C22×C17 | semidirect |
| 41. C3×C7⋊D7 | D3×C17 | semidirect |
| 44. #64425 | C2×C3×C17 | semidirect |
| 45. #64418 | C2×C3×C17 | semidirect |
| 54. C3×C72 | C2×D3×C17 | semidirect |
| 56. #3862 | C22×C3×C17 | semidirect |
| 65. C7⋊D7 | C3×D3×C17 | semidirect |
| 72. C3×C17 | #64418⋊C2 | direct (N × H) |
| 73. C72 | C2×C3×D3×C17 | semidirect |
| 90. C17 | C3×#64418⋊C2 | direct (N × H) |
| 108. C3 | C17×#64418⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C17×#64418 | 2 |
| C3×C17×#64425 | 2 |
| C3×D72×C17 | 3 |
| C17×#64418⋊C2 | 3 |
| C3×#64418⋊C2 | 17 |
| C2×C3×D3×C17 | 49 |