Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
216 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 64 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×C7×C13×Dic7 | C3 | semidirect |
| 3. C13×#10596873 | C3 | direct (N × H) |
| 4. C3×C13×#3861 | C4 | semidirect |
| 9. C7×C13×Dic7 | C32 | semidirect |
| 10. C3×C72×C13 | C3×C4 | semidirect |
| 11. C13×#3861 | C3×C4 | semidirect |
| 12. C3×#10596873 | C13 | direct (N × H) |
| 18. C3×C13×Dic7 | ΓL(1,𝔽8) | semidirect |
| 25. C72×C13 | C32×C4 | semidirect |
| 26. C3×C7×Dic7 | C3×C13 | semidirect |
| 27. #10596873 | C3×C13 | direct (N × H) |
| 35. C3×#3861 | C4×C13 | semidirect |
| 37. C13×Dic7 | C3×ΓL(1,𝔽8) | semidirect |
| 41. C3×C7×C13 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 42. C3×C7×C13 | C4×ΓL(1,𝔽8) | semidirect |
| 49. C7×Dic7 | C32×C13 | semidirect |
| 55. C3×C72 | C3×C4×C13 | semidirect |
| 56. #3861 | C3×C4×C13 | semidirect |
| 63. C7×C13 | C3×ΓL(1,𝔽8)⋊C4 | semidirect |
| 64. C7×C13 | C3×C4×ΓL(1,𝔽8) | semidirect |
| 66. C3×Dic7 | C13×ΓL(1,𝔽8) | semidirect |
| 75. C72 | C32×C4×C13 | semidirect |
| 83. C3×C13 | #10596873 | direct (N × H) |
| 86. Dic7 | C3×C13×ΓL(1,𝔽8) | semidirect |
| 89. C3×C7 | C13×ΓL(1,𝔽8)⋊C4 | semidirect |
| 90. C3×C7 | C4×C13×ΓL(1,𝔽8) | semidirect |
| 98. C13 | C3×#10596873 | direct (N × H) |
| 103. C7 | C3×C13×ΓL(1,𝔽8)⋊C4 | semidirect |
| 104. C7 | C3×C4×C13×ΓL(1,𝔽8) | semidirect |
| 109. C3 | C13×#10596873 | 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×#3861 | 2 |
| C3×C7×C13×Dic7 | 3 |
| C13×#10596873 | 3 |
| C3×C4×C13×ΓL(1,𝔽8) | 7 |
| C3×C13×ΓL(1,𝔽8)⋊C4 | 7 |
| C3×#10596873 | 13 |