Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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×#14583814 | C2 | semidirect |
| 2. C2×C4×Dic346 | C2 | semidirect |
| 3. #26011688 | C2 | direct (N × H) |
| 4. C2×C4⋊#13063436 | C2 | semidirect |
| 5. C2×#19149600 | C2 | semidirect |
| 9. C2×#14583814 | C22 | semidirect |
| 12. C4×Dic346 | C22 | semidirect |
| 16. C4⋊#13063436 | C22 | semidirect |
| 17. #19149600 | C22 | semidirect |
| 26. C2×Dic346 | D4 | semidirect |
| 53. Dic346 | C2×D4 | semidirect |
| 70. C2×C4×C173 | SD16 | semidirect |
| 87. C4×C173 | C2×SD16 | semidirect |
| 93. C2×C173 | #460 | semidirect |
| 97. C173 | C2×#460 | semidirect |
| 167. C2×C4 | #14583814 | semidirect |
| 187. C4 | C2×#14583814 | semidirect |
| 191. C2 | #26011688 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583814 | 2 |
| C2×C4×Dic346 | 2 |
| #26011688 | 2 |
| C2×C4⋊#13063436 | 2 |
| C2×#19149600 | 2 |
| C2×#127×C173 | 2 |
| C2×#460 | 173 |