Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 5. #26011700 | C2 | direct (N × H) |
| 75. C2×Dic173 | Q16 | semidirect |
| 104. Dic173 | C2×Q16 | semidirect |
| 105. C2×C173 | #462 | semidirect |
| 109. C173 | C2×#462 | semidirect |
| 215. C2 | #26011700 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic692 | 2 |
| C22×#14583816 | 2 |
| C2×#19149677 | 2 |
| C2×#19149644 | 2 |
| #26011700 | 2 |
| C2×#19149608 | 2 |
| C2×#19149602 | 2 |
| C2×#103×C173 | 2 |
| C2×#462 | 173 |