Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 244 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. D4×#13063443 | C2 | semidirect |
| 2. #26012507 | C2 | semidirect |
| 3. C2×C22⋊#13063443 | C2 | semidirect |
| 5. C22×#13063443 | C22 | semidirect |
| 6. C4⋊#13063443 | C22 | semidirect |
| 8. C22⋊#13063443 | C22 | semidirect |
| 9. C4×#13063443 | C22 | semidirect |
| 30. C2×D4×C173 | C8 | semidirect |
| 45. C23×C173 | C2×C8 | semidirect |
| 48. D4×C173 | C2×C8 | semidirect |
| 49. C2×C4×C173 | C2×C8 | semidirect |
| 69. C173 | #2972 | semidirect |
| 88. C2×D4 | #13063443 | semidirect |
| 105. C23 | C2×#13063443 | semidirect |
| 108. D4 | C2×#13063443 | semidirect |
| 118. C2×C4 | C2×#13063443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#13063443 | 2 |
| #26012507 | 2 |
| C2×C22⋊#13063443 | 2 |
| C2×D4×Dic173 | 2 |
| #2972 | 173 |