Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
272 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 9. #19149746 | C4 | semidirect |
| 10. C4⋊#13063443 | C4 | semidirect |
| 16. C4×#13063436 | C4 | semidirect |
| 17. C8×Dic173 | C4 | semidirect |
| 18. C8×Dic173 | C4 | semidirect |
| 19. C4×C8×C173 | C4 | semidirect |
| 57. #13063436 | C4⋊C4 | semidirect |
| 62. C8×C173 | C4⋊C4 | semidirect |
| 70. C4×C173 | #97 | semidirect |
| 74. Dic173 | #97 | semidirect |
| 82. C173 | #1770 | semidirect |
| 101. C4×C8 | #10621924 | semidirect |
| 145. C8 | C4⋊#10621924 | semidirect |
| 157. 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 |
| C4×C4⋊#10621924 | 2 |
| (C2×#10621924)⋊C8 | 2 |
| C4×C8×D173 | 2 |
| #1770 | 173 |