Finite Group DatabasebetaFinite Group Databasebeta← C19×(#64418⋊C2)⋊C3 #45692000
Order 33516.
152 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | (#64418⋊C2)⋊C3 |
| commutator, cosocle, hypocenter | #3862 | C22×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C72×C19 | C2×C3×D3 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C19 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×#64418⋊C3 | C2 | semidirect |
| 2. C19×ΓL(1,𝔽8)⋊AGL(1,𝔽7) | C2 | semidirect |
| 3. C19×#64418⋊C2 | C3 | semidirect |
| 5. C19×ΓL(1,𝔽8)2 | C22 | semidirect |
| 6. C19×#64418 | C2×C3 | semidirect |
| 9. C19×#64425 | C2×C3 | semidirect |
| 10. C19×#64424 | D3 | semidirect |
| 12. C19×#3862 | C22×C3 | semidirect |
| 13. C19×#3861 | C2×D3 | semidirect |
| 16. C19×C7⋊D7 | C3×D3 | semidirect |
| 18. (#64418⋊C2)⋊C3 | C19 | direct (N × H) |
| 21. C72×C19 | C2×C3×D3 | semidirect |
| 22. ΓL(1,𝔽8)⋊AGL(1,𝔽7) | C2×C19 | semidirect |
| 23. #64418⋊C3 | C2×C19 | semidirect |
| 33. #64418⋊C2 | C3×C19 | semidirect |
| 35. ΓL(1,𝔽8)2 | C22×C19 | semidirect |
| 43. #64425 | C2×C3×C19 | semidirect |
| 44. #64424 | D3×C19 | semidirect |
| 47. #64418 | C2×C3×C19 | semidirect |
| 56. #3862 | C22×C3×C19 | semidirect |
| 57. #3861 | C2×D3×C19 | semidirect |
| 67. C7⋊D7 | C3×D3×C19 | semidirect |
| 75. C72 | C2×C3×D3×C19 | semidirect |
| 92. C19 | (#64418⋊C2)⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#64418⋊C3 | 2 |
| C19×ΓL(1,𝔽8)⋊AGL(1,𝔽7) | 2 |
| C19×#64418⋊C2 | 3 |
| C19×#64423⋊C2 | 3 |
| (#64418⋊C2)⋊C3 | 19 |
| C2×C3×D3×C19 | 49 |