Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
128 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 128 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. #26039478 | C2 | direct (N × H) |
| 4. C7×#11717942 | C22 | semidirect |
| 9. C2×C7×D91 | C9 | semidirect |
| 12. C2×#11717942 | D7 | semidirect |
| 16. C2×C72×C13 | C2×C9 | semidirect |
| 17. C7×D91 | C2×C9 | semidirect |
| 22. #11717942 | C2×D7 | semidirect |
| 24. C72×C13 | C22×C9 | semidirect |
| 33. C2×D91 | C7⋊C9 | semidirect |
| 46. C2×C7×C13 | C2×C7⋊C9 | semidirect |
| 47. C2×C7×C13 | C9×D7 | semidirect |
| 48. D91 | C2×C7⋊C9 | semidirect |
| 57. C2×C72 | D13⋊C9 | semidirect |
| 60. C7×C13 | C22×C7⋊C9 | semidirect |
| 61. C7×C13 | C2×C9×D7 | semidirect |
| 69. C72 | C2×D13⋊C9 | semidirect |
| 79. C2×C13 | D7×C7⋊C9 | semidirect |
| 88. C2×C7 | (C13⋊C9)⋊D7 | semidirect |
| 89. C2×C7 | #13109897 | semidirect |
| 91. C13 | C2×D7×C7⋊C9 | semidirect |
| 95. C7 | C2×(C13⋊C9)⋊D7 | semidirect |
| 96. C7 | C2×#13109897 | semidirect |
| 102. C2 | #26039478 | 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 |
| #26039478 | 2 |
| C2×C3×C7×D91 | 3 |
| C2×#13109897 | 7 |
| C2×(C13⋊C9)⋊D7 | 7 |
| C2×D7×C7⋊C9 | 13 |