Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26011865 | C2 | semidirect |
| 3. D4×#13063436 | C2 | semidirect |
| 4. #26011241 | C2 | semidirect |
| 5. #26011237 | C2 | semidirect |
| 6. #26011234 | C2 | semidirect |
| 7. #474×C173 | C2 | semidirect |
| 52. #13063436 | D8 | semidirect |
| 57. D4×C173 | SD16 | semidirect |
| 85. C173 | #1665 | semidirect |
| 88. #474 | D173 | semidirect |
| 139. D4 | #14583813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011865 | 2 |
| #26011686 | 2 |
| D4×#13063436 | 2 |
| #26011241 | 2 |
| #26011237 | 2 |
| #26011234 | 2 |
| #474×C173 | 2 |
| #1665 | 173 |