Finite Group DatabasebetaFinite Group DatabasebetaOrder 22176.
168 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 63 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. D5544 | C2 | semidirect |
| 8. C7×C9×C11×C16 | C2 | semidirect |
| 16. C9×C11×C16 | D7 | semidirect |
| 20. C7×C11×C16 | D9 | semidirect |
| 23. C7×C9×C16 | D11 | semidirect |
| 28. C7×C9×C11 | D16 | semidirect |
| 55. C11×C16 | D63 | semidirect |
| 61. C9×C16 | D77 | semidirect |
| 67. C7×C16 | D99 | semidirect |
| 68. C9×C11 | D112 | semidirect |
| 74. C7×C11 | D144 | semidirect |
| 79. C7×C9 | D176 | semidirect |
| 102. C16 | D693 | semidirect |
| 107. C11 | D1008 | semidirect |
| 108. C9 | D1232 | semidirect |
| 111. C7 | D1584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5544 | 2 |
| D3696 | 3 |
| D1584 | 7 |
| D1008 | 11 |
| C7×C9×C11×C16 | 2 |