Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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×#19149620 | C2 | semidirect |
| 2. C2×#19149618 | C2 | semidirect |
| 3. #26011728 | C2 | semidirect |
| 4. #26011724 | C2 | semidirect |
| 5. #26011318 | C2 | semidirect |
| 6. #26011293 | C2 | semidirect |
| 7. #357×C173 | C2 | semidirect |
| 33. #14583801 | D4 | semidirect |
| 79. C173 | #2218 | semidirect |
| 87. #357 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149620 | 2 |
| C2×#19149618 | 2 |
| #26011728 | 2 |
| #26011724 | 2 |
| #26011318 | 2 |
| #26011293 | 2 |
| #357×C173 | 2 |
| #2218 | 173 |