Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
272 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 76 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. C2×#19149750 | C2 | semidirect |
| 2. C2×#19149749 | C2 | semidirect |
| 4. #26012367 | C2 | semidirect |
| 102. C173 | #1811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149750 | 2 |
| C2×#19149749 | 2 |
| #26012462 | 2 |
| #26012367 | 2 |
| C2×M16×D173 | 2 |
| #1811 | 173 |