Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
328 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 8. #19149734 | C4 | semidirect |
| 9. #19149733 | C4 | semidirect |
| 10. C8×#10621924 | C4 | semidirect |
| 15. C4×#13063436 | C4 | semidirect |
| 16. C8×Dic173 | C4 | semidirect |
| 17. C8×Dic173 | C4 | semidirect |
| 18. C4×C8×C173 | C4 | semidirect |
| 63. C173 | #1726 | semidirect |
| 81. C4×C8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012450 | 2 |
| C2×#19149733 | 2 |
| C2×C8×#10621924 | 2 |
| #26012427 | 2 |
| C4×C8×D173 | 2 |
| #1726 | 173 |