Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#19149605 | C2 | semidirect |
| 3. C4×C4⋊Dic173 | C2 | semidirect |
| 4. C4×M16×C173 | C2 | semidirect |
| 6. #19149679 | C4 | semidirect |
| 7. #19149676 | C4 | semidirect |
| 8. #19149667 | C4 | semidirect |
| 40. M16×C173 | D4 | semidirect |
| 81. C4×C173 | #104 | semidirect |
| 92. C173 | #1980 | semidirect |
| 96. C4×M16 | D173 | semidirect |
| 127. M16 | D692 | semidirect |
| 176. C4 | #19149605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| C2×#19149605 | 2 |
| C4×C4⋊Dic173 | 2 |
| C4×M16×C173 | 2 |
| #1980 | 173 |