Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 91 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. C22×#14583813 | C2 | semidirect |
| 2. C2×#19149655 | C2 | semidirect |
| 4. C2×#19149601 | C2 | semidirect |
| 5. C2×#19149591 | C2 | semidirect |
| 6. #26011253 | C2 | semidirect |
| 7. C2×#103×C173 | C2 | semidirect |
| 51. C2×#13063436 | D4 | semidirect |
| 53. C4⋊Dic173 | D4 | semidirect |
| 62. C2×Q8×C173 | D4 | semidirect |
| 84. C22×D173 | SD16 | semidirect |
| 157. C173 | #2000 | semidirect |
| 162. C2×#103 | D173 | semidirect |
| 194. C2×Q8 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583813 | 2 |
| C2×#19149655 | 2 |
| C2×#19149654 | 2 |
| C2×#19149601 | 2 |
| C2×#19149591 | 2 |
| #26011253 | 2 |
| C2×#103×C173 | 2 |
| #2000 | 173 |