Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
300 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 145 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×#19153200 | C2 | semidirect |
| 2. #26039471 | C2 | direct (N × H) |
| 3. #26039471 | C2 | direct (N × H) |
| 5. #19153200 | C22 | semidirect |
| 11. C2×C72×D13 | C9 | semidirect |
| 20. C2×C72×C13 | C2×C9 | semidirect |
| 21. C72×D13 | C2×C9 | semidirect |
| 22. C72×D13 | C2×C9 | semidirect |
| 30. C72×C13 | C22×C9 | semidirect |
| 40. C2×C7×D13 | C7⋊C9 | semidirect |
| 41. C2×C7×D13 | C7⋊C9 | semidirect |
| 53. C2×C7×C13 | C2×C7⋊C9 | semidirect |
| 54. C2×C7×C13 | C2×C7⋊C9 | semidirect |
| 55. C7×D13 | C2×C7⋊C9 | semidirect |
| 56. C7×D13 | C2×C7⋊C9 | semidirect |
| 57. C7×D13 | C2×C7⋊C9 | semidirect |
| 58. C7×D13 | C2×C7⋊C9 | semidirect |
| 70. C2×C72 | D13⋊C9 | semidirect |
| 71. C7×C13 | C22×C7⋊C9 | semidirect |
| 72. C7×C13 | C22×C7⋊C9 | semidirect |
| 80. C2×D13 | #89204 | semidirect |
| 81. C72 | C2×D13⋊C9 | semidirect |
| 92. C2×C13 | C2×#89204 | semidirect |
| 93. D13 | C2×#89204 | semidirect |
| 94. D13 | C2×#89204 | semidirect |
| 104. C2×C7 | #13109896 | semidirect |
| 105. C2×C7 | #13109896 | semidirect |
| 106. C13 | C22×#89204 | semidirect |
| 109. C7 | C2×#13109896 | semidirect |
| 110. C7 | C2×#13109896 | semidirect |
| 118. C2 | #26039471 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153200 | 2 |
| #26039471 | 2 |
| C2×C3×C72×D13 | 3 |
| C2×#13109896 | 7 |
| C22×#89204 | 13 |