Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
164 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
| 11. C4⋊#13063436 | C4 | semidirect |
| 14. C4⋊C8×C173 | C4 | semidirect |
| 65. C173 | #1285 | semidirect |
| 75. C4⋊C8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012513 | 2 |
| C4×C4⋊#10621924 | 2 |
| #26011547 | 2 |
| #1285 | 173 |