Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
480 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 165 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. #26011246 | C2 | semidirect |
| 4. #26011245 | C2 | semidirect |
| 5. #336×C173 | C2 | semidirect |
| 10. C2×#14583809 | C4 | semidirect |
| 30. C2×#13063436 | C2×C4 | semidirect |
| 37. C2×C8×C173 | C2×C4 | semidirect |
| 49. C2×Dic173 | M16 | semidirect |
| 57. C2×C4×C173 | M16 | semidirect |
| 84. C173 | #1728 | semidirect |
| 90. #336 | D173 | semidirect |
| 120. C2×C8 | C4×D173 | semidirect |
| 141. C2×C4 | #14583809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583809 | 2 |
| C2×C42×D173 | 2 |
| #26011246 | 2 |
| #26011245 | 2 |
| #336×C173 | 2 |
| #1728 | 173 |