Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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. #26011969 | C2 | semidirect |
| 3. #26011592 | C2 | semidirect |
| 4. SD16×Dic173 | C2 | semidirect |
| 5. #26011529 | C2 | semidirect |
| 6. #26011500 | C2 | semidirect |
| 8. #26011446 | C2 | semidirect |
| 12. Q8×Dic173 | C22 | semidirect |
| 20. #19149613 | C22 | semidirect |
| 21. #19149611 | C22 | semidirect |
| 22. #19149603 | C22 | semidirect |
| 24. #19149589 | C22 | semidirect |
| 25. C8×Dic173 | C22 | semidirect |
| 28. C2×SD16×C173 | C4 | semidirect |
| 50. C2×Q8×C173 | C2×C4 | semidirect |
| 58. SD16×C173 | C2×C4 | semidirect |
| 59. SD16×C173 | C2×C4 | semidirect |
| 60. C2×C8×C173 | C2×C4 | semidirect |
| 103. C173 | #2949 | semidirect |
| 116. C2×SD16 | Dic173 | semidirect |
| 139. C2×Q8 | C2×Dic173 | semidirect |
| 148. SD16 | C2×Dic173 | semidirect |
| 149. SD16 | C2×Dic173 | semidirect |
| 152. C2×C8 | C2×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011969 | 2 |
| #26011966 | 2 |
| #26011592 | 2 |
| SD16×Dic173 | 2 |
| #26011529 | 2 |
| #26011500 | 2 |
| #26011496 | 2 |
| #26011446 | 2 |
| C22×SD16×C173 | 2 |
| #2949 | 173 |