Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#19149710 | C2 | semidirect |
| 3. C4×#14583826 | C2 | semidirect |
| 4. #26011710 | C2 | semidirect |
| 5. #26011703 | C2 | semidirect |
| 6. #26011515 | C2 | semidirect |
| 7. #26011500 | C2 | semidirect |
| 8. #26011496 | C2 | semidirect |
| 9. C2×#124×C173 | C2 | semidirect |
| 13. C2×#14583816 | C22 | semidirect |
| 15. C2×#14583813 | C22 | semidirect |
| 19. C4×Dic346 | C22 | semidirect |
| 20. C4×D692 | C22 | semidirect |
| 25. C4⋊#13063436 | C22 | semidirect |
| 26. #19149603 | C22 | semidirect |
| 125. C173 | #3040 | semidirect |
| 129. C2×#124 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149710 | 2 |
| C2×#19149705 | 2 |
| C4×#14583826 | 2 |
| #26011710 | 2 |
| #26011703 | 2 |
| #26011515 | 2 |
| #26011500 | 2 |
| #26011496 | 2 |
| C2×#124×C173 | 2 |
| #3040 | 173 |