Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
556 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 373 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. #26011449 | C2 | semidirect |
| 4. #26011446 | C2 | semidirect |
| 5. M16×Dic173 | C2 | semidirect |
| 6. C2×#19149589 | C2 | semidirect |
| 8. #19149686 | C4 | semidirect |
| 21. #131×C173 | C4 | semidirect |
| 25. #14583810 | C2×C4 | semidirect |
| 26. C2×#13063436 | C2×C4 | semidirect |
| 39. M16×C173 | C2×C4 | semidirect |
| 40. C2×C8×C173 | C2×C4 | semidirect |
| 68. C173 | #2875 | semidirect |
| 79. #131 | Dic173 | semidirect |
| 100. M16 | C2×Dic173 | semidirect |
| 104. C2×C8 | C2×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149686 | 2 |
| #41×Dic173 | 2 |
| #26011449 | 2 |
| #26011446 | 2 |
| M16×Dic173 | 2 |
| C2×#19149589 | 2 |
| C2×#131×C173 | 2 |
| #2875 | 173 |