Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
384 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19149612 | C2 | semidirect |
| 3. C2×#19149600 | C2 | semidirect |
| 4. C2×#19149599 | C2 | semidirect |
| 5. C2×C4×#13063436 | C2 | semidirect |
| 6. #26011393 | C2 | semidirect |
| 7. #390×C173 | C2 | semidirect |
| 11. C2×#14583811 | C4 | semidirect |
| 69. #13063436 | C22⋊C4 | semidirect |
| 84. C2×C4×C173 | D8 | semidirect |
| 120. C173 | #1970 | semidirect |
| 128. #390 | D173 | semidirect |
| 203. C2×C4 | #14583811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583811 | 2 |
| C2×#19149612 | 2 |
| C2×#19149600 | 2 |
| C2×#19149599 | 2 |
| C2×C4×#13063436 | 2 |
| #26011393 | 2 |
| #390×C173 | 2 |
| #1970 | 173 |