Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
152 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 57. C8×C173 | Q16 | semidirect |
| 71. C173 | #1584 | semidirect |
| 129. C8 | #14583816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011621 | 2 |
| C4×#14583816 | 2 |
| #26011243 | 2 |
| Q8⋊#13063436 | 2 |
| #26011221 | 2 |
| #26011212 | 2 |
| C8×Q8×C173 | 2 |
| #1584 | 173 |