Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26011869 | C2 | semidirect |
| 4. #26011840 | C2 | semidirect |
| 5. #26011700 | C2 | semidirect |
| 6. #26011699 | C2 | semidirect |
| 94. C2×Dic173 | Q16 | semidirect |
| 133. C173 | #3209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012043 | 2 |
| C2×#19149677 | 2 |
| #26011869 | 2 |
| #26011840 | 2 |
| #26011700 | 2 |
| #26011699 | 2 |
| #26011649 | 2 |
| #26011647 | 2 |
| #26011646 | 2 |
| #26011541 | 2 |
| #451×C173 | 2 |
| #3209 | 173 |