Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
332 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 157 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. #19149603 | C4 | direct (N × H) |
| 14. C4×Q8×C173 | C4 | semidirect |
| 48. Q8×C173 | C42 | semidirect |
| 70. C4×C173 | #103 | semidirect |
| 80. C173 | C4×#103 | semidirect |
| 90. C4×Q8 | Dic173 | semidirect |
| 125. Q8 | C4×Dic173 | semidirect |
| 152. C4 | #19149603 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149603 | 2 |
| C2×C4×#13063436 | 2 |
| C4×C4⋊Dic173 | 2 |
| #26011253 | 2 |
| C2×C4×Q8×C173 | 2 |
| C4×#103 | 173 |