Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 181 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. #26011553 | C2 | semidirect |
| 3. #26011542 | C2 | semidirect |
| 4. #26011519 | C2 | semidirect |
| 6. C2×C4×#13063436 | C2 | semidirect |
| 7. C4×M16×C173 | C2 | semidirect |
| 77. C173 | #2922 | semidirect |
| 84. C4×M16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14583826 | 2 |
| #26011553 | 2 |
| #26011542 | 2 |
| #26011519 | 2 |
| #26011459 | 2 |
| C2×C4×#13063436 | 2 |
| C4×M16×C173 | 2 |
| #2922 | 173 |