Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
928 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 381 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. #26011397 | C2 | direct (N × H) |
| 8. C22×Dic346 | C4 | semidirect |
| 22. C2×Dic346 | C2×C4 | semidirect |
| 37. C22×C4×C173 | Q8 | semidirect |
| 62. C2×C4×C173 | C2×Q8 | semidirect |
| 77. C2×C173 | #391 | semidirect |
| 83. C173 | C2×#391 | semidirect |
| 120. C22×C4 | Dic346 | semidirect |
| 146. C2×C4 | C2×Dic346 | semidirect |
| 161. C2 | #26011397 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic346 | 2 |
| C22×C4⋊Dic173 | 2 |
| #26011397 | 2 |
| C2×#19149586 | 2 |
| C22×C42×C173 | 2 |
| C2×#391 | 173 |