Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
156 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 61 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×#19153199 | C2 | semidirect |
| 2. #26039457 | C2 | direct (N × H) |
| 3. #26039457 | C2 | direct (N × H) |
| 5. #19153199 | C22 | semidirect |
| 11. C2×C7×C13×D7 | C9 | semidirect |
| 21. C2×C72×C13 | C2×C9 | semidirect |
| 22. C7×C13×D7 | C2×C9 | semidirect |
| 23. C7×C13×D7 | C2×C9 | semidirect |
| 32. C72×C13 | C22×C9 | semidirect |
| 44. C2×C13×D7 | C7⋊C9 | semidirect |
| 56. C2×C7×D7 | C13⋊C9 | semidirect |
| 60. C2×C7×C13 | D7⋊C9 | semidirect |
| 61. C2×C7×C13 | C2×C7⋊C9 | semidirect |
| 62. C13×D7 | C2×C7⋊C9 | semidirect |
| 63. C13×D7 | C2×C7⋊C9 | semidirect |
| 74. C2×C72 | C2×C13⋊C9 | semidirect |
| 75. C7×D7 | C2×C13⋊C9 | semidirect |
| 76. C7×D7 | C2×C13⋊C9 | semidirect |
| 78. C7×C13 | C2×D7⋊C9 | semidirect |
| 79. C7×C13 | C22×C7⋊C9 | semidirect |
| 89. C72 | C22×C13⋊C9 | semidirect |
| 100. C2×D7 | #11717942 | semidirect |
| 103. C2×C13 | #11725076 | semidirect |
| 113. C2×C7 | #13109901 | semidirect |
| 114. C2×C7 | C2×#11717942 | semidirect |
| 115. D7 | C2×#11717942 | semidirect |
| 116. D7 | C2×#11717942 | semidirect |
| 117. C13 | C2×#11725076 | semidirect |
| 121. C7 | C2×#13109901 | semidirect |
| 122. C7 | C22×#11717942 | semidirect |
| 130. C2 | #26039457 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153199 | 2 |
| #26039457 | 2 |
| C2×C3×C7×C13×D7 | 3 |
| C22×#11717942 | 7 |
| C2×#13109901 | 7 |
| C2×#11725076 | 13 |