Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
260 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 22. #14583835 | Q8 | semidirect |
| 82. C173 | #1997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012494 | 2 |
| C4×#14583835 | 2 |
| #26012371 | 2 |
| C2×#19149677 | 2 |
| #1997 | 173 |