Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
| 2. C22×#14583813 | C2 | semidirect |
| 4. #26011713 | C2 | semidirect |
| 5. #26011691 | C2 | semidirect |
| 6. #26011518 | C2 | semidirect |
| 7. #26011495 | C2 | semidirect |
| 8. #26011485 | C2 | semidirect |
| 9. #519×C173 | C2 | semidirect |
| 13. C2×#14583816 | C22 | semidirect |
| 16. C2×#14583813 | C22 | semidirect |
| 23. C4⋊#13063436 | C22 | semidirect |
| 24. #19149602 | C22 | semidirect |
| 26. #19149599 | C22 | semidirect |
| 29. C4×Q8×C173 | C22 | semidirect |
| 55. C2×Q8×C173 | D4 | semidirect |
| 116. C173 | #3043 | semidirect |
| 121. #519 | D173 | semidirect |
| 142. C4×Q8 | C2×D173 | semidirect |
| 156. C2×Q8 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149710 | 2 |
| C22×#14583813 | 2 |
| #26012060 | 2 |
| #26011713 | 2 |
| #26011691 | 2 |
| #26011518 | 2 |
| #26011495 | 2 |
| #26011485 | 2 |
| #519×C173 | 2 |
| #3043 | 173 |