Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
360 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 145 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. #26011893 | C2 | semidirect |
| 3. #26011892 | C2 | semidirect |
| 4. #26011891 | C2 | semidirect |
| 5. #26011890 | C2 | semidirect |
| 9. #499×C173 | C2 | semidirect |
| 75. D173 | #499 | direct (N × H) |
| 76. C173 | C2×#499 | semidirect |
| 83. #499 | D173 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×D173 | 2 |
| #26011893 | 2 |
| #26011892 | 2 |
| #26011891 | 2 |
| #26011890 | 2 |
| #107×D173 | 2 |
| #106×D173 | 2 |
| C4×C8×D173 | 2 |
| #499×C173 | 2 |
| C2×#499 | 173 |