Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
308 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 14. Q8×Dic173 | C4 | semidirect |
| 16. C4×Dic346 | C4 | semidirect |
| 18. #19149644 | C4 | semidirect |
| 23. C4×Q8×C173 | C4 | semidirect |
| 67. Dic346 | C4⋊C4 | semidirect |
| 86. Q8×C173 | C4⋊C4 | semidirect |
| 103. C4×C173 | #103 | semidirect |
| 109. Dic173 | #103 | semidirect |
| 119. C173 | #1803 | semidirect |
| 133. C4×Q8 | #10621924 | semidirect |
| 185. Q8 | C4⋊#10621924 | semidirect |
| 229. C4 | #19149742 | 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×#19149742 | 2 |
| #26012437 | 2 |
| #26012364 | 2 |
| C4×Q8×D173 | 2 |
| #1803 | 173 |