Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
222 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 60 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. #26012498 | C2 | semidirect |
| 4. C2×#19149733 | C2 | semidirect |
| 5. #26012367 | C2 | semidirect |
| 6. #26012361 | C2 | semidirect |
| 21. #19149604 | C4 | semidirect |
| 22. #19149602 | C4 | semidirect |
| 23. #19149600 | C4 | semidirect |
| 24. #102×C173 | C4 | semidirect |
| 105. C173 | #1938 | semidirect |
| 127. #102 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012498 | 2 |
| C2×#19149743 | 2 |
| #26012465 | 2 |
| C2×#19149733 | 2 |
| #26012367 | 2 |
| #26012361 | 2 |
| #26011484 | 2 |
| #1938 | 173 |