Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
320 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 70 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. #26012496 | C2 | semidirect |
| 2. C2×#19149744 | C2 | semidirect |
| 3. #26012427 | C2 | semidirect |
| 11. #19149676 | C4 | semidirect |
| 12. #19149668 | C4 | semidirect |
| 16. C4⋊Q8×C173 | C4 | semidirect |
| 21. C4×#10621924 | D4 | semidirect |
| 71. C173 | #1963 | semidirect |
| 79. C4⋊Q8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012496 | 2 |
| C2×#19149744 | 2 |
| #26012427 | 2 |
| #26012042 | 2 |
| #1963 | 173 |