Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
266 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 81 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. C4×#14583810 | C2 | semidirect |
| 3. #26011221 | C2 | semidirect |
| 4. #26011218 | C2 | semidirect |
| 5. #423×C173 | C2 | semidirect |
| 54. Dic346 | M16 | semidirect |
| 56. D692 | M16 | semidirect |
| 102. C173 | #1489 | semidirect |
| 105. #423 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14583826 | 2 |
| C4×#14583810 | 2 |
| #26011221 | 2 |
| #26011218 | 2 |
| #423×C173 | 2 |
| #1489 | 173 |