Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
248 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 248 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 |
|---|---|---|
| 21. C2×Dic346 | C8 | semidirect |
| 80. C173 | #1461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149644 | 2 |
| #26011541 | 2 |
| #26011217 | 2 |
| #26011216 | 2 |
| #324×C173 | 2 |
| #1461 | 173 |