Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1488 conjugacy classes of subgroups; only the 762 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 762 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. #26012559 | C2 | direct (N × H) |
| 2. C2×Q8×#10621924 | C2 | semidirect |
| 5. Q8×#10621924 | C22 | semidirect |
| 10. C22×Dic346 | C4 | semidirect |
| 11. C2×Q8×D173 | C4 | semidirect |
| 12. C2×Q8×D173 | C4 | semidirect |
| 16. C22×Q8×C173 | C4 | semidirect |
| 23. C2×Dic346 | C2×C4 | semidirect |
| 25. Q8×D173 | C2×C4 | semidirect |
| 33. C2×Q8×C173 | C2×C4 | semidirect |
| 66. C2×C173 | #519 | semidirect |
| 69. D173 | #519 | semidirect |
| 71. C173 | C2×#519 | semidirect |
| 82. C22×Q8 | #10621924 | semidirect |
| 96. C2×Q8 | C2×#10621924 | semidirect |
| 141. C2 | #26012559 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012559 | 2 |
| C2×Q8×#10621924 | 2 |
| C2×#19149758 | 2 |
| C22×Q8×D173 | 2 |
| C2×#519 | 173 |