Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
180 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 86 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. #26012355 | C2 | semidirect |
| 3. #26012353 | C2 | semidirect |
| 18. C2×#13063436 | C8 | semidirect |
| 60. C173 | #1564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012507 | 2 |
| #26012355 | 2 |
| #26012353 | 2 |
| C2×C8×Dic173 | 2 |
| #1564 | 173 |