Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
138 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. C4⋊#14583801 | C2 | semidirect |
| 5. #26011266 | C2 | semidirect |
| 6. C16×Dic173 | C2 | semidirect |
| 7. C4⋊C16×C173 | C2 | semidirect |
| 66. C173 | #2164 | semidirect |
| 70. C4⋊C16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011445 | 2 |
| C4⋊#14583801 | 2 |
| #26011270 | 2 |
| #26011266 | 2 |
| C16×Dic173 | 2 |
| C4⋊C16×C173 | 2 |
| #2164 | 173 |