Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
128 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 50 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. C7×#13109897 | C2 | semidirect |
| 2. C7×#13109901 | C2 | semidirect |
| 3. C7×#13109903 | C2 | semidirect |
| 5. C7×#11717942 | C22 | semidirect |
| 10. #13109897⋊C2 | C7 | direct (N × H) |
| 11. C7×D7×D13 | C9 | semidirect |
| 15. #13109903 | C2×C7 | semidirect |
| 16. #13109901 | C2×C7 | semidirect |
| 17. #13109897 | C2×C7 | semidirect |
| 20. C7×D91 | C2×C9 | semidirect |
| 21. C7×C13×D7 | C2×C9 | semidirect |
| 22. C72×D13 | C2×C9 | semidirect |
| 28. #11717942 | C22×C7 | semidirect |
| 30. C72×C13 | C22×C9 | semidirect |
| 42. D7×D13 | C7×C9 | semidirect |
| 56. D91 | C2×C7×C9 | semidirect |
| 59. C7×D13 | D7⋊C9 | semidirect |
| 60. C7×D13 | C2×C7×C9 | semidirect |
| 61. C13×D7 | C2×C7×C9 | semidirect |
| 73. C7×D7 | D13⋊C9 | semidirect |
| 75. C7×C13 | C2×D7⋊C9 | semidirect |
| 76. C7×C13 | C22×C7×C9 | semidirect |
| 85. C72 | C2×D13⋊C9 | semidirect |
| 99. D13 | C7×D7⋊C9 | semidirect |
| 112. D7 | C7×D13⋊C9 | semidirect |
| 113. C13 | C2×C7×D7⋊C9 | semidirect |
| 117. C7 | #13109897⋊C2 | direct (N × H) |
| 118. C7 | C2×C7×D13⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#13109897 | 2 |
| C7×#13109901 | 2 |
| C7×#13109903 | 2 |
| C3×C7×D7×D13 | 3 |
| C2×C7×D13⋊C9 | 7 |
| #13109897⋊C2 | 7 |
| C2×C7×D7⋊C9 | 13 |