Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 166 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×#19149767 | C2 | semidirect |
| 2. C2×#19149766 | C2 | semidirect |
| 3. #26012524 | C2 | semidirect |
| 4. #26012518 | C2 | semidirect |
| 5. #26012496 | C2 | semidirect |
| 6. #26012466 | C2 | semidirect |
| 7. #26012465 | C2 | semidirect |
| 8. C4×D173⋊C8 | C2 | semidirect |
| 40. D173⋊C8 | D4 | semidirect |
| 107. Dic173 | #131 | semidirect |
| 115. C173 | #2931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149767 | 2 |
| C2×#19149766 | 2 |
| #26012524 | 2 |
| #26012518 | 2 |
| #26012496 | 2 |
| #26012466 | 2 |
| #26012465 | 2 |
| C4×D173⋊C8 | 2 |
| #26012040 | 2 |
| #2931 | 173 |