Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
230 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 77 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×C4×#13063436 | C2 | semidirect |
| 3. #26011221 | C2 | semidirect |
| 4. #26011218 | C2 | semidirect |
| 5. #432×C173 | C2 | semidirect |
| 90. C173 | #1494 | semidirect |
| 93. #432 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012025 | 2 |
| C2×C4×#13063436 | 2 |
| #26011221 | 2 |
| #26011218 | 2 |
| #432×C173 | 2 |
| #1494 | 173 |