Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 78 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. #19149733 | C4 | semidirect |
| 9. C8×#10621924 | C4 | semidirect |
| 13. #19149589 | C4 | semidirect |
| 14. C4×#13063436 | C4 | semidirect |
| 15. C8×Dic173 | C4 | semidirect |
| 16. #97×C173 | C4 | semidirect |
| 61. C173 | #1747 | semidirect |
| 75. #97 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012454 | 2 |
| #26012360 | 2 |
| #26012359 | 2 |
| #26012358 | 2 |
| #26011448 | 2 |
| #1747 | 173 |