Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
440 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 74 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. #26012461 | C2 | semidirect |
| 2. #26012334 | C2 | semidirect |
| 6. C22⋊#13063443 | C22 | semidirect |
| 61. C23×C173 | M16 | semidirect |
| 91. C173 | #1462 | semidirect |
| 142. C23 | #14583835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012461 | 2 |
| #26012334 | 2 |
| C22×C22⋊Dic173 | 2 |
| #1462 | 173 |