Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26012103 | C2 | semidirect |
| 3. #26011833 | C2 | semidirect |
| 4. #26011792 | C2 | semidirect |
| 5. #26011697 | C2 | semidirect |
| 7. #26011593 | C2 | semidirect |
| 8. C4×#14583815 | C2 | semidirect |
| 9. #433×C173 | C2 | semidirect |
| 13. #19149679 | C22 | semidirect |
| 15. #19149671 | C22 | semidirect |
| 18. C4×Dic346 | C22 | semidirect |
| 24. #19149613 | C22 | semidirect |
| 25. #19149611 | C22 | semidirect |
| 26. #19149604 | C22 | semidirect |
| 27. #19149604 | C22 | semidirect |
| 31. C4⋊C8×C173 | C22 | semidirect |
| 33. #97×C173 | C22 | semidirect |
| 34. C4×C8×C173 | C22 | semidirect |
| 102. C173 | #3123 | semidirect |
| 112. #433 | D173 | semidirect |
| 130. C4⋊C8 | C2×D173 | semidirect |
| 136. #97 | C2×D173 | semidirect |
| 137. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012103 | 2 |
| #26011965 | 2 |
| #26011833 | 2 |
| #26011792 | 2 |
| #26011697 | 2 |
| #26011644 | 2 |
| #26011593 | 2 |
| C4×#14583815 | 2 |
| #433×C173 | 2 |
| #3123 | 173 |