Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 492 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×#19149766 | C2 | semidirect |
| 2. #26012526 | C2 | semidirect |
| 3. #26012522 | C2 | semidirect |
| 4. D4×#13063443 | C2 | semidirect |
| 5. D173⋊(C4⋊C8) | C2 | semidirect |
| 6. #26012465 | C2 | semidirect |
| 7. C4×#14583836 | C2 | semidirect |
| 32. #14583836 | D4 | semidirect |
| 92. C4×C173 | #131 | semidirect |
| 103. C173 | #2935 | semidirect |
| 201. C4 | #19149766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149766 | 2 |
| #26012526 | 2 |
| #26012522 | 2 |
| D4×#13063443 | 2 |
| D173⋊(C4⋊C8) | 2 |
| #26012465 | 2 |
| C4×#14583836 | 2 |
| #26012039 | 2 |
| #2935 | 173 |