Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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. D173⋊M32 | C2 | semidirect |
| 2. C2×#19149747 | C2 | semidirect |
| 3. #26012408 | C2 | semidirect |
| 4. #26012407 | C2 | semidirect |
| 7. #19149754 | C22 | semidirect |
| 11. #19149747 | C22 | semidirect |
| 14. #19149701 | C4 | semidirect |
| 18. Q16×D173 | C4 | semidirect |
| 20. D8×D173 | C4 | semidirect |
| 22. #135×C173 | C4 | semidirect |
| 37. Dic692 | C2×C4 | semidirect |
| 42. D1384 | C2×C4 | semidirect |
| 50. Q16×C173 | C2×C4 | semidirect |
| 52. D8×C173 | C2×C4 | semidirect |
| 102. D173 | #360 | semidirect |
| 103. C173 | C2×#360 | semidirect |
| 116. #135 | #10621924 | semidirect |
| 141. Q16 | C2×#10621924 | semidirect |
| 148. D8 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊M32 | 2 |
| C2×#19149747 | 2 |
| #26012408 | 2 |
| #26012407 | 2 |
| #135×D173 | 2 |
| C2×#360 | 173 |