Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
252 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26011223 | C2 | semidirect |
| 43. Dic346 | M16 | semidirect |
| 76. C173 | #1491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic346 | 2 |
| #26011548 | 2 |
| #26011223 | 2 |
| C4×M16×C173 | 2 |
| #1491 | 173 |