Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
168 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 2. C3×C72×Dic19 | C3 | semidirect |
| 3. Dic19⋊#3862 | C3 | direct (N × H) |
| 4. C3×C19⋊#3862 | C4 | semidirect |
| 9. C72×Dic19 | C32 | semidirect |
| 10. C19⋊#3862 | C3×C4 | semidirect |
| 11. C3×C72×C19 | C3×C4 | semidirect |
| 17. C3×C7×Dic19 | ΓL(1,𝔽8) | semidirect |
| 18. C3×C7×Dic19 | ΓL(1,𝔽8) | semidirect |
| 23. C72×C19 | C32×C4 | semidirect |
| 34. C7×Dic19 | C3×ΓL(1,𝔽8) | semidirect |
| 35. C7×Dic19 | C3×ΓL(1,𝔽8) | semidirect |
| 38. C3×C7×C19 | C4×ΓL(1,𝔽8) | semidirect |
| 39. C3×C7×C19 | C4×ΓL(1,𝔽8) | semidirect |
| 50. C3×Dic19 | #3862 | semidirect |
| 54. C3×C72 | (C19⋊C3)⋊C4 | semidirect |
| 57. C7×C19 | C3×C4×ΓL(1,𝔽8) | semidirect |
| 58. C7×C19 | C3×C4×ΓL(1,𝔽8) | semidirect |
| 69. Dic19 | C3×#3862 | semidirect |
| 72. C3×C19 | C4×#3862 | semidirect |
| 74. C72 | C3×(C19⋊C3)⋊C4 | semidirect |
| 86. C3×C7 | #13097582 | semidirect |
| 87. C3×C7 | #13097583 | semidirect |
| 90. C19 | C3×C4×#3862 | semidirect |
| 99. C7 | C3×#13097582 | semidirect |
| 100. C7 | C3×#13097583 | semidirect |
| 105. C3 | Dic19⋊#3862 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C19⋊#3862 | 2 |
| C3×C72×Dic19 | 3 |
| Dic19⋊#3862 | 3 |
| C3×#13097583 | 7 |
| C3×#13097582 | 7 |
| C3×C4×#3862 | 19 |