Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
172 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 172 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 |
|---|---|---|
| 6. #19149734 | C4 | semidirect |
| 11. C4⋊#13063436 | C4 | semidirect |
| 14. C4⋊C8×C173 | C4 | semidirect |
| 62. C173 | #1300 | semidirect |
| 71. C4⋊C8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14583836 | 2 |
| #26012427 | 2 |
| #26011547 | 2 |
| #1300 | 173 |