Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. #26011871 | C2 | semidirect |
| 4. #26011236 | C2 | semidirect |
| 5. #335×C173 | C2 | semidirect |
| 36. D692 | Q16 | semidirect |
| 63. C173 | #1669 | semidirect |
| 68. #335 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011871 | 2 |
| #26011772 | 2 |
| C8×D692 | 2 |
| #26011236 | 2 |
| #335×C173 | 2 |
| #1669 | 173 |