Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
126 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 22. #14583829 | Q8 | semidirect |
| 59. C173 | #2183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012412 | 2 |
| C4⋊#14583829 | 2 |
| #26012380 | 2 |
| #26012379 | 2 |
| #26012377 | 2 |
| #26011615 | 2 |
| #2183 | 173 |