Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
178 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #26011213 | C2 | semidirect |
| 5. #26011212 | C2 | semidirect |
| 6. C8×#13063436 | C2 | semidirect |
| 7. #322×C173 | C2 | semidirect |
| 64. C173 | #1454 | semidirect |
| 71. #322 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011542 | 2 |
| #26011213 | 2 |
| #26011212 | 2 |
| C8×#13063436 | 2 |
| #322×C173 | 2 |
| #1454 | 173 |