Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
392 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 138 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. #26012367 | C2 | semidirect |
| 73. D173 | #341 | semidirect |
| 74. C173 | C2×#341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D173⋊M16 | 2 |
| #26012367 | 2 |
| C22×C8×D173 | 2 |
| C2×#341 | 173 |