Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
224 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 3. #26012332 | C2 | semidirect |
| 4. C8×#13063443 | C2 | semidirect |
| 25. #14583809 | C8 | semidirect |
| 34. #13063443 | M16 | semidirect |
| 42. #13063436 | C2×C8 | semidirect |
| 46. C8×C173 | C2×C8 | semidirect |
| 61. C173 | C8×M16 | semidirect |
| 108. C8 | D173⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012509 | 2 |
| C4×D173⋊C8 | 2 |
| #26012332 | 2 |
| C8×#13063443 | 2 |
| #26011443 | 2 |
| C8×M16 | 173 |