Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1168 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 150 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. C22×C22⋊#10621924 | C2 | semidirect |
| 2. C2×(C2×#10621924)⋊C4 | C2 | semidirect |
| 9. C22×D692 | C4 | semidirect |
| 10. C22×C22⋊D173 | C4 | semidirect |
| 14. C22×D4×C173 | C4 | semidirect |
| 19. C22×#10621924 | D4 | semidirect |
| 59. C22×D173 | C22⋊C4 | semidirect |
| 67. C2×Dic173 | C22⋊C4 | semidirect |
| 72. C23×C173 | C22⋊C4 | semidirect |
| 76. C2×C4×C173 | C22⋊C4 | semidirect |
| 107. C173 | #1438 | semidirect |
| 117. C22×D4 | #10621924 | semidirect |
| 170. C23 | C22⋊#10621924 | semidirect |
| 184. C2×C4 | C22⋊#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#10621924 | 2 |
| C2×(C2×#10621924)⋊C4 | 2 |
| C22×D4×D173 | 2 |
| #1438 | 173 |