Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26011290 | C2 | semidirect |
| 4. #26011289 | C2 | semidirect |
| 5. #356×C173 | C2 | semidirect |
| 83. D173 | #356 | direct (N × H) |
| 84. C173 | C2×#356 | semidirect |
| 90. #356 | D173 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D173 | 2 |
| #101×D173 | 2 |
| #26011290 | 2 |
| #26011289 | 2 |
| #356×C173 | 2 |
| C2×#356 | 173 |