Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 3. #26011241 | C2 | semidirect |
| 4. Q8⋊#13063436 | C2 | semidirect |
| 6. C8×#13063436 | C2 | semidirect |
| 7. C8×Q8×C173 | C2 | semidirect |
| 25. #14583813 | C8 | direct (N × H) |
| 50. #13063436 | C2×C8 | semidirect |
| 52. Q8×C173 | C2×C8 | semidirect |
| 60. C8×C173 | SD16 | semidirect |
| 77. C173 | C8×SD16 | semidirect |
| 79. C8×Q8 | D173 | semidirect |
| 121. Q8 | C8×D173 | semidirect |
| 138. C8 | #14583813 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14583813 | 2 |
| C8×D692 | 2 |
| #26011241 | 2 |
| Q8⋊#13063436 | 2 |
| #26011218 | 2 |
| C8×#13063436 | 2 |
| C8×Q8×C173 | 2 |
| C8×SD16 | 173 |