Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
252 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 68 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. #26012341 | C2 | semidirect |
| 45. 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 |
|---|---|
| #26012512 | 2 |
| C4×#14583835 | 2 |
| #26012341 | 2 |
| C2×#19149644 | 2 |
| #1491 | 173 |