Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
402 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 168 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×#13063443 | C2 | semidirect |
| 2. #26012525 | C2 | semidirect |
| 3. #26012513 | C2 | semidirect |
| 4. C4×#14583836 | C2 | semidirect |
| 36. #13063443 | #41 | semidirect |
| 45. Q8×C173 | M16 | semidirect |
| 63. C173 | #2971 | semidirect |
| 100. Q8 | #14583836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#13063443 | 2 |
| #26012525 | 2 |
| #26012513 | 2 |
| C4×#14583836 | 2 |
| C4×#14583827 | 2 |
| #2971 | 173 |