Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
360 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 94 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. C4×#14583835 | C2 | semidirect |
| 3. #26012371 | C2 | semidirect |
| 6. #19149739 | C4 | semidirect |
| 19. #14583835 | C2×C4 | semidirect |
| 90. Dic173 | #100 | semidirect |
| 99. C173 | C4×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149739 | 2 |
| C4×#14583835 | 2 |
| #26012371 | 2 |
| C2×#19149639 | 2 |
| C4×#100 | 173 |