Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
364 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 2. #26011620 | C2 | semidirect |
| 3. #26011615 | C2 | semidirect |
| 33. C2×#13063436 | Q8 | semidirect |
| 83. C173 | #2960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012044 | 2 |
| #26011620 | 2 |
| #26011615 | 2 |
| #26011517 | 2 |
| #26011514 | 2 |
| #26011449 | 2 |
| #26011447 | 2 |
| C2×C8×Dic173 | 2 |
| #424×C173 | 2 |
| #2960 | 173 |