Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D692 | C2 | semidirect |
| 3. #26011843 | C2 | semidirect |
| 4. #26011823 | C2 | semidirect |
| 5. #26011721 | C2 | semidirect |
| 6. #26011697 | C2 | semidirect |
| 7. #26011631 | C2 | semidirect |
| 8. C4×#14583813 | C2 | semidirect |
| 9. #26011556 | C2 | semidirect |
| 10. #103×D173 | C2 | semidirect |
| 11. #475×C173 | C2 | semidirect |
| 85. D692 | SD16 | semidirect |
| 98. Q8×C173 | #41 | semidirect |
| 128. C173 | #3298 | semidirect |
| 134. #475 | D173 | semidirect |
| 213. Q8 | #14583827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D692 | 2 |
| #26012144 | 2 |
| #26011843 | 2 |
| #26011823 | 2 |
| #26011721 | 2 |
| #26011697 | 2 |
| #26011631 | 2 |
| C4×#14583813 | 2 |
| #26011556 | 2 |
| #103×D173 | 2 |
| #475×C173 | 2 |
| #3298 | 173 |