Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
272 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 13. #19149746 | C4 | semidirect |
| 14. C4⋊#13063443 | C4 | semidirect |
| 21. #19149590 | C4 | semidirect |
| 22. #19149589 | C4 | semidirect |
| 23. #19149589 | C4 | semidirect |
| 24. #97×C173 | C4 | semidirect |
| 72. #13063436 | C4⋊C4 | semidirect |
| 77. C8×C173 | C4⋊C4 | semidirect |
| 98. C173 | #1771 | semidirect |
| 121. #97 | #10621924 | semidirect |
| 176. C8 | C4⋊#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊(C4⋊C8) | 2 |
| C2×#19149733 | 2 |
| C2×C8×#10621924 | 2 |
| C4×C4⋊#10621924 | 2 |
| (C2×#10621924)⋊C8 | 2 |
| #97×D173 | 2 |
| #1771 | 173 |