Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
180 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 69 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. C8×C173 | Q16 | semidirect |
| 63. C173 | #1707 | semidirect |
| 115. C8 | #14583816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011894 | 2 |
| #26011889 | 2 |
| #26011870 | 2 |
| #26011843 | 2 |
| #26011841 | 2 |
| C8×#13063436 | 2 |
| #498×C173 | 2 |
| #1707 | 173 |