Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26012044 | C2 | semidirect |
| 5. #26011263 | C2 | semidirect |
| 6. #26011250 | C2 | semidirect |
| 7. H(3,ℤ/4)×C173 | C2 | semidirect |
| 28. C2×Dic346 | Q8 | semidirect |
| 29. C2×D692 | Q8 | semidirect |
| 102. C173 | #2031 | semidirect |
| 110. H(3,ℤ/4) | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012044 | 2 |
| #26011509 | 2 |
| C2×#19149605 | 2 |
| #26011464 | 2 |
| #26011263 | 2 |
| #26011250 | 2 |
| H(3,ℤ/4)×C173 | 2 |
| #2031 | 173 |