Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #26011531 | C2 | semidirect |
| 5. #26011260 | C2 | semidirect |
| 6. #26011251 | C2 | semidirect |
| 7. #384×C173 | C2 | semidirect |
| 19. #19149607 | C4 | semidirect |
| 38. #14583810 | C2×C4 | semidirect |
| 58. C42×C173 | C2×C4 | semidirect |
| 61. Dic346 | C4⋊C4 | semidirect |
| 63. D692 | C4⋊C4 | semidirect |
| 112. C173 | #1859 | semidirect |
| 118. #384 | D173 | semidirect |
| 171. C42 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011972 | 2 |
| #26011531 | 2 |
| C2×#19149607 | 2 |
| #26011490 | 2 |
| #26011260 | 2 |
| #26011251 | 2 |
| #384×C173 | 2 |
| #1859 | 173 |