Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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. #26012219 | C2 | semidirect |
| 4. #26011238 | C2 | semidirect |
| 5. Q8⋊#13063436 | C2 | semidirect |
| 6. #26011221 | C2 | semidirect |
| 52. Dic346 | SD16 | semidirect |
| 90. C173 | #1626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012219 | 2 |
| #26011837 | 2 |
| #26011688 | 2 |
| #26011238 | 2 |
| Q8⋊#13063436 | 2 |
| #26011221 | 2 |
| #460×C173 | 2 |
| #1626 | 173 |