Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
620 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 620 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. C2×#19149606 | C2 | semidirect |
| 2. #26011492 | C2 | semidirect |
| 3. C2×#19149596 | C2 | semidirect |
| 4. #26011394 | C2 | semidirect |
| 6. C2×#14583810 | C22 | semidirect |
| 7. C2×C4⋊Dic173 | C22 | semidirect |
| 9. C2×C4×Dic173 | C22 | semidirect |
| 16. H(5,𝔽2)×C173 | C4 | semidirect |
| 70. Q8×C173 | C22⋊C4 | semidirect |
| 77. D4×C173 | C22⋊C4 | semidirect |
| 112. C173 | #1792 | semidirect |
| 121. H(5,𝔽2) | Dic173 | semidirect |
| 177. Q8 | C22⋊Dic173 | semidirect |
| 184. D4 | C22⋊Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149606 | 2 |
| #26011492 | 2 |
| C2×#19149596 | 2 |
| #26011394 | 2 |
| C2×H(5,𝔽2)×C173 | 2 |
| #1792 | 173 |