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. #26011533 | C2 | semidirect |
| 5. #26011360 | C2 | semidirect |
| 6. #26011252 | C2 | semidirect |
| 7. #343×C173 | C2 | semidirect |
| 20. #19149605 | C4 | semidirect |
| 48. C4×Dic173 | C2×C4 | semidirect |
| 54. M16×C173 | C2×C4 | semidirect |
| 61. Dic346 | C4⋊C4 | semidirect |
| 63. D692 | C4⋊C4 | semidirect |
| 112. C173 | #1859 | semidirect |
| 119. #343 | D173 | semidirect |
| 155. M16 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011972 | 2 |
| #26011533 | 2 |
| C2×#19149605 | 2 |
| #26011493 | 2 |
| #26011360 | 2 |
| #26011252 | 2 |
| #343×C173 | 2 |
| #1859 | 173 |