Finite Group DatabasebetaFinite Group Databasebeta← C2×C3⋊((C49⋊C3)⋊D13) #37524259
Order 22932.
132 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 38 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. C2×C3×C13×C49⋊C3 | C2 | semidirect |
| 2. C3⋊((C49⋊C3)⋊D13) | C2 | direct (N × H) |
| 3. C2×D1911 | C3 | semidirect |
| 5. C3×C13×C49⋊C3 | C22 | semidirect |
| 6. D1911 | C2×C3 | semidirect |
| 8. C2×C13×C49⋊C3 | D3 | semidirect |
| 10. C2×C3×C13×C49 | C2×C3 | semidirect |
| 13. C3×C13×C49 | C22×C3 | semidirect |
| 15. C13×C49⋊C3 | C2×D3 | semidirect |
| 19. C2×C13×C49 | C3×D3 | semidirect |
| 23. C2×C3×C49⋊C3 | D13 | semidirect |
| 26. C13×C49 | C2×C3×D3 | semidirect |
| 35. C3×C49⋊C3 | C2×D13 | semidirect |
| 37. C2×C3×C49 | C3×D13 | semidirect |
| 40. C2×C49⋊C3 | D39 | semidirect |
| 53. C3×C49 | C2×C3×D13 | semidirect |
| 55. C49⋊C3 | C2×D39 | semidirect |
| 59. C2×C49 | C3×D39 | semidirect |
| 66. C2×C3×C13 | D49⋊C3 | semidirect |
| 71. C49 | C2×C3×D39 | semidirect |
| 79. C3×C13 | C2×D49⋊C3 | semidirect |
| 82. C2×C13 | C3⋊(D49⋊C3) | semidirect |
| 91. C13 | C2×C3⋊(D49⋊C3) | semidirect |
| 99. C2×C3 | (C49⋊C3)⋊D13 | semidirect |
| 104. C3 | C2×(C49⋊C3)⋊D13 | semidirect |
| 106. C2 | C3⋊((C49⋊C3)⋊D13) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C13×C49⋊C3 | 2 |
| C3⋊((C49⋊C3)⋊D13) | 2 |
| C2×D1911 | 3 |
| C2×(C49⋊C3)⋊D13 | 3 |
| C2×C3⋊(ΓL(1,𝔽8)⋊D13) | 7 |
| C2×C3⋊(D49⋊C3) | 13 |