Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
144 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #26011321 | C2 | semidirect |
| 4. #26011320 | C2 | semidirect |
| 5. #368×C173 | C2 | semidirect |
| 52. D173 | #368 | direct (N × H) |
| 53. C173 | C2×#368 | semidirect |
| 59. #368 | D173 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D173 | 2 |
| #108×D173 | 2 |
| #26011321 | 2 |
| #26011320 | 2 |
| #368×C173 | 2 |
| C2×#368 | 173 |