Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19149702 | C2 | semidirect |
| 2. #26012163 | C2 | semidirect |
| 3. #26011868 | C2 | semidirect |
| 4. #26011728 | C2 | semidirect |
| 5. #26011691 | C2 | semidirect |
| 6. #26011639 | C2 | semidirect |
| 7. C8×D692 | C2 | semidirect |
| 8. C4×Q16×C173 | C2 | semidirect |
| 48. Q16×C173 | D4 | semidirect |
| 88. C4×C173 | #135 | semidirect |
| 97. C173 | #3287 | semidirect |
| 105. C4×Q16 | D173 | semidirect |
| 138. Q16 | D692 | semidirect |
| 187. C4 | #19149702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149702 | 2 |
| #26012163 | 2 |
| #26011868 | 2 |
| #26011728 | 2 |
| #26011691 | 2 |
| #26011639 | 2 |
| C8×D692 | 2 |
| C4×Q16×C173 | 2 |
| #3287 | 173 |