Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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. #26011549 | C2 | semidirect |
| 3. #26011545 | C2 | semidirect |
| 4. #26011519 | C2 | semidirect |
| 5. #26011517 | C2 | semidirect |
| 7. M16×Dic173 | C2 | semidirect |
| 8. C2×#19149589 | C2 | semidirect |
| 93. C173 | #2923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic173 | 2 |
| #26011549 | 2 |
| #26011545 | 2 |
| #26011519 | 2 |
| #26011517 | 2 |
| #26011458 | 2 |
| M16×Dic173 | 2 |
| C2×#19149589 | 2 |
| #408×C173 | 2 |
| #2923 | 173 |