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. #26011842 | C2 | semidirect |
| 4. #26011823 | C2 | semidirect |
| 5. #26011776 | C2 | semidirect |
| 6. #26011719 | C2 | semidirect |
| 7. #26011696 | C2 | semidirect |
| 8. #26011628 | C2 | semidirect |
| 9. C8×D692 | C2 | semidirect |
| 10. #103×D173 | C2 | semidirect |
| 11. C4×SD16×C173 | C2 | semidirect |
| 82. D692 | SD16 | semidirect |
| 94. Q8×C173 | #41 | semidirect |
| 128. C173 | #3298 | semidirect |
| 138. C4×SD16 | D173 | semidirect |
| 213. Q8 | #14583826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D692 | 2 |
| #26012146 | 2 |
| #26011842 | 2 |
| #26011823 | 2 |
| #26011776 | 2 |
| #26011719 | 2 |
| #26011696 | 2 |
| #26011628 | 2 |
| C8×D692 | 2 |
| #103×D173 | 2 |
| C4×SD16×C173 | 2 |
| #3298 | 173 |