Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
332 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 80 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. D173⋊(C22⋊C8) | C2 | semidirect |
| 2. #26012337 | C2 | semidirect |
| 3. #26012334 | C2 | semidirect |
| 22. C2×C22⋊D173 | C8 | semidirect |
| 52. C2×Dic173 | C2×C8 | semidirect |
| 60. C23×C173 | C2×C8 | semidirect |
| 97. C173 | #1459 | semidirect |
| 147. C23 | D173⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊(C22⋊C8) | 2 |
| #26012337 | 2 |
| #26012334 | 2 |
| C2×C4×C22⋊D173 | 2 |
| #1459 | 173 |