Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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×#19149608 | C2 | semidirect |
| 4. #26011360 | C2 | semidirect |
| 5. #26011254 | C2 | semidirect |
| 6. #26011253 | C2 | semidirect |
| 11. D4×Dic173 | C4 | semidirect |
| 82. D4×C173 | C4⋊C4 | semidirect |
| 115. Dic173 | #102 | semidirect |
| 124. C173 | #1802 | semidirect |
| 193. D4 | #14583805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic173 | 2 |
| C2×#19149608 | 2 |
| C2×#19149600 | 2 |
| #26011360 | 2 |
| #26011254 | 2 |
| #26011253 | 2 |
| C2×#102×C173 | 2 |
| #1802 | 173 |