Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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×C7×#11717942 | C2 | semidirect |
| 2. #26039469 | C2 | direct (N × H) |
| 3. #26039469 | C2 | direct (N × H) |
| 5. C7×#11717942 | C22 | semidirect |
| 11. C2×C13×C7⋊D7 | C9 | semidirect |
| 14. C2×#11717942 | D7 | semidirect |
| 20. C2×C72×C13 | C2×C9 | semidirect |
| 21. C13×C7⋊D7 | C2×C9 | semidirect |
| 22. C13×C7⋊D7 | C2×C9 | semidirect |
| 29. #11717942 | C2×D7 | semidirect |
| 31. C72×C13 | C22×C9 | semidirect |
| 58. C2×C7⋊D7 | C13⋊C9 | semidirect |
| 60. C2×C7×C13 | D7⋊C9 | semidirect |
| 61. C2×C7×C13 | C9×D7 | semidirect |
| 77. C2×C72 | C2×C13⋊C9 | semidirect |
| 78. C7⋊D7 | C2×C13⋊C9 | semidirect |
| 79. C7⋊D7 | C2×C13⋊C9 | semidirect |
| 81. C7×C13 | C2×D7⋊C9 | semidirect |
| 82. C7×C13 | C2×C9×D7 | semidirect |
| 92. C72 | C22×C13⋊C9 | semidirect |
| 109. C2×C13 | (C7⋊C9)⋊D7 | semidirect |
| 117. C2×C7 | D7×C13⋊C9 | semidirect |
| 118. C2×C7 | #13109901 | semidirect |
| 125. C13 | C2×(C7⋊C9)⋊D7 | semidirect |
| 129. C7 | C2×D7×C13⋊C9 | semidirect |
| 130. C7 | C2×#13109901 | semidirect |
| 138. C2 | #26039469 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#11717942 | 2 |
| #26039469 | 2 |
| C2×C3×C13×C7⋊D7 | 3 |
| C2×#13109901 | 7 |
| C2×D7×C13⋊C9 | 7 |
| C2×(C7⋊C9)⋊D7 | 13 |