Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #26011899 | C2 | semidirect |
| 4. #26011898 | C2 | semidirect |
| 5. #26011892 | C2 | semidirect |
| 6. #26011891 | C2 | semidirect |
| 48. #14583810 | Q8 | semidirect |
| 72. M16×C173 | Q8 | semidirect |
| 124. C173 | #3166 | semidirect |
| 176. M16 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012044 | 2 |
| C2×#19149670 | 2 |
| #26011899 | 2 |
| #26011898 | 2 |
| #26011892 | 2 |
| #26011891 | 2 |
| #26011534 | 2 |
| #26011533 | 2 |
| #26011531 | 2 |
| M16×Dic173 | 2 |
| #428×C173 | 2 |
| #3166 | 173 |