Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 51. Q8×C173 | Q16 | semidirect |
| 69. C173 | #3363 | semidirect |
| 117. Q8 | Dic692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic346 | 2 |
| #26012220 | 2 |
| #26011842 | 2 |
| #26011787 | 2 |
| #26011702 | 2 |
| C4×Dic692 | 2 |
| C8×Q8×C173 | 2 |
| #3363 | 173 |