Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
292 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 11. #19149746 | C4 | semidirect |
| 12. C4⋊#13063443 | C4 | semidirect |
| 16. C4⋊#13063436 | C4 | semidirect |
| 17. #19149608 | C4 | semidirect |
| 18. C4⋊C8×C173 | C4 | semidirect |
| 71. C4×C173 | #97 | semidirect |
| 75. Dic173 | #97 | semidirect |
| 83. C173 | #1767 | semidirect |
| 101. C4⋊C8 | #10621924 | semidirect |
| 159. C4 | #19149733 | 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 |
| C42×#10621924 | 2 |
| (C2×#10621924)⋊C8 | 2 |
| C4⋊C8×D173 | 2 |
| #1767 | 173 |