Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
272 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 108 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. C4×#13063443 | C4 | semidirect |
| 12. C4×#13063443 | C4 | semidirect |
| 16. C4⋊#13063436 | C4 | semidirect |
| 17. #19149608 | C4 | semidirect |
| 18. C4⋊C8×C173 | C4 | semidirect |
| 44. #13063443 | C4⋊C4 | semidirect |
| 67. C4×C173 | #97 | semidirect |
| 71. Dic173 | #97 | semidirect |
| 79. C173 | #1770 | semidirect |
| 94. C4⋊C8 | #10621924 | semidirect |
| 151. C4 | #19149733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149733 | 2 |
| C4×D173⋊C8 | 2 |
| C4×C4⋊#10621924 | 2 |
| (C2×#10621924)⋊C8 | 2 |
| C4⋊C8×D173 | 2 |
| #1770 | 173 |