Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#19149710 | C2 | semidirect |
| 3. C2×#19149606 | C2 | semidirect |
| 4. C2×#19149605 | C2 | semidirect |
| 5. #26011398 | C2 | semidirect |
| 6. #26011259 | C2 | semidirect |
| 7. C2×#137×C173 | C2 | semidirect |
| 45. #14583810 | D4 | semidirect |
| 64. C2×Q8×C173 | D4 | semidirect |
| 73. M16×C173 | D4 | semidirect |
| 144. C173 | #2007 | semidirect |
| 147. C2×#137 | D173 | semidirect |
| 191. C2×Q8 | C22⋊D173 | semidirect |
| 210. M16 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149710 | 2 |
| #26012069 | 2 |
| C2×#19149606 | 2 |
| C2×#19149605 | 2 |
| #26011398 | 2 |
| #26011259 | 2 |
| C2×#137×C173 | 2 |
| #2007 | 173 |