Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
348 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#19149734 | C2 | semidirect |
| 4. C2×C4×#13063443 | C2 | semidirect |
| 5. #26012357 | C2 | semidirect |
| 6. #26012357 | C2 | semidirect |
| 10. C2×#14583836 | C4 | semidirect |
| 15. #19149736 | C4 | semidirect |
| 60. #13063443 | C22⋊C4 | semidirect |
| 73. C2×Dic173 | M16 | semidirect |
| 93. C2×C4×C173 | M16 | semidirect |
| 125. C173 | #1753 | semidirect |
| 215. C2×C4 | #14583836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583836 | 2 |
| C2×#19149736 | 2 |
| C2×#19149734 | 2 |
| C2×C4×#13063443 | 2 |
| #26012357 | 2 |
| #26011338 | 2 |
| #1753 | 173 |