Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19149712 | C2 | semidirect |
| 2. C2×#19149687 | C2 | semidirect |
| 4. #26012067 | C2 | semidirect |
| 5. #26011750 | C2 | semidirect |
| 6. #26011738 | C2 | semidirect |
| 7. #26011733 | C2 | semidirect |
| 8. #26011721 | C2 | semidirect |
| 9. #26011485 | C2 | semidirect |
| 10. C2×#19149602 | C2 | semidirect |
| 11. #428×C173 | C2 | semidirect |
| 77. M16×C173 | D4 | semidirect |
| 143. C173 | #3063 | semidirect |
| 153. #428 | D173 | semidirect |
| 210. M16 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149712 | 2 |
| C2×#19149687 | 2 |
| #26012072 | 2 |
| #26012067 | 2 |
| #26011750 | 2 |
| #26011738 | 2 |
| #26011733 | 2 |
| #26011721 | 2 |
| #26011485 | 2 |
| C2×#19149602 | 2 |
| #428×C173 | 2 |
| #3063 | 173 |