Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
184 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 3. #26012378 | C2 | semidirect |
| 4. C16×#10621924 | C2 | semidirect |
| 8. #19149754 | C4 | semidirect |
| 9. #19149753 | C4 | semidirect |
| 14. C2×#14583801 | C4 | semidirect |
| 15. C16×D173 | C4 | semidirect |
| 16. C16×D173 | C4 | semidirect |
| 19. C2×C16×C173 | C4 | semidirect |
| 64. C173 | #2108 | semidirect |
| 82. C2×C16 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊M32 | 2 |
| #26012454 | 2 |
| #26012378 | 2 |
| C16×#10621924 | 2 |
| C2×C16×D173 | 2 |
| #2108 | 173 |