Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 3. #26011316 | C2 | semidirect |
| 4. #26011295 | C2 | semidirect |
| 6. #26011267 | C2 | semidirect |
| 7. C4×Q16×C173 | C2 | semidirect |
| 10. #19149622 | C4 | semidirect |
| 27. #14583801 | C2×C4 | semidirect |
| 30. Q16×C173 | C2×C4 | semidirect |
| 67. C173 | #2175 | semidirect |
| 70. C4×Q16 | D173 | semidirect |
| 92. Q16 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149622 | 2 |
| C4×D1384 | 2 |
| #26011316 | 2 |
| #26011295 | 2 |
| #26011291 | 2 |
| #26011267 | 2 |
| C4×Q16×C173 | 2 |
| #2175 | 173 |