Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
324 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 88 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. #19149679 | C4 | semidirect |
| 16. #19149677 | C4 | semidirect |
| 20. C4⋊Q8×C173 | C4 | semidirect |
| 77. C4×C173 | #103 | semidirect |
| 81. Dic173 | #103 | semidirect |
| 89. C173 | #1981 | semidirect |
| 101. C4⋊Q8 | #10621924 | semidirect |
| 172. 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 |
| C4×C4⋊#10621924 | 2 |
| C4⋊Q8×D173 | 2 |
| #1981 | 173 |