Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
152 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 6. C4×#13063443 | C4 | semidirect |
| 13. #19149590 | C4 | semidirect |
| 14. #97×C173 | C4 | semidirect |
| 58. C173 | #1288 | semidirect |
| 69. #97 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14583836 | 2 |
| #26012436 | 2 |
| #26011546 | 2 |
| #1288 | 173 |