Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
416 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #26011776 | C2 | direct (N × H) |
| 33. C2×Q8×C173 | Q8 | semidirect |
| 53. Q8×C173 | C2×Q8 | semidirect |
| 78. C2×C173 | #475 | semidirect |
| 82. C173 | C2×#475 | semidirect |
| 110. C2×Q8 | Dic346 | semidirect |
| 133. Q8 | C2×Dic346 | semidirect |
| 161. C2 | #26011776 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149679 | 2 |
| #26011776 | 2 |
| C2×#19149610 | 2 |
| C2×C4⋊#13063436 | 2 |
| C2×#19149603 | 2 |
| C2×C4×Q8×C173 | 2 |
| C2×#475 | 173 |