Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
172 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 48 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. D8×#10621924 | C2 | semidirect |
| 2. #26012418 | C2 | semidirect |
| 3. #26012403 | C2 | semidirect |
| 4. #26012378 | C2 | semidirect |
| 12. D2768 | C4 | semidirect |
| 13. #19149620 | C4 | semidirect |
| 15. D16×C173 | C4 | semidirect |
| 23. D1384 | C2×C4 | semidirect |
| 26. #14583801 | C2×C4 | semidirect |
| 27. D8×C173 | C2×C4 | semidirect |
| 28. C16×C173 | C2×C4 | semidirect |
| 53. C173 | #2177 | semidirect |
| 64. D16 | #10621924 | semidirect |
| 74. D8 | C2×#10621924 | semidirect |
| 82. C16 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#10621924 | 2 |
| #26012418 | 2 |
| #26012403 | 2 |
| #26012378 | 2 |
| D16×D173 | 2 |
| #2177 | 173 |