Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 2. C2×#19149679 | C2 | semidirect |
| 3. #26011864 | C2 | semidirect |
| 4. #26011842 | C2 | semidirect |
| 5. #26011697 | C2 | semidirect |
| 6. #26011632 | C2 | semidirect |
| 7. #431×C173 | C2 | semidirect |
| 72. C2×C4×C173 | SD16 | semidirect |
| 100. C173 | #3206 | semidirect |
| 108. #431 | D173 | semidirect |
| 173. C2×C4 | #14583815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| C2×#19149679 | 2 |
| #26011864 | 2 |
| #26011842 | 2 |
| #26011697 | 2 |
| #26011632 | 2 |
| #431×C173 | 2 |
| #3206 | 173 |