Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 1. C2×#19149702 | C2 | semidirect |
| 2. C2×#19149622 | C2 | semidirect |
| 3. C2×D2768 | C2 | semidirect |
| 4. #26011728 | C2 | semidirect |
| 5. #26011291 | C2 | semidirect |
| 6. #26011270 | C2 | semidirect |
| 7. #358×C173 | C2 | semidirect |
| 35. D1384 | D4 | semidirect |
| 43. Q16×C173 | D4 | semidirect |
| 89. C173 | #2186 | semidirect |
| 95. #358 | D173 | semidirect |
| 123. Q16 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149702 | 2 |
| C2×#19149622 | 2 |
| C2×D2768 | 2 |
| #26011728 | 2 |
| #26011291 | 2 |
| #26011270 | 2 |
| #358×C173 | 2 |
| #2186 | 173 |