Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
424 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 165 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. #26011889 | C2 | semidirect |
| 3. #26011888 | C2 | semidirect |
| 4. #26011887 | C2 | semidirect |
| 7. #498×C173 | C2 | semidirect |
| 31. C8×D173 | Q8 | semidirect |
| 52. #13063436 | C2×Q8 | semidirect |
| 57. C8×C173 | C2×Q8 | semidirect |
| 69. D173 | #498 | direct (N × H) |
| 70. C173 | C2×#498 | semidirect |
| 76. #498 | D173 | direct (N × H) |
| 128. C8 | Q8×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D173 | 2 |
| #26011889 | 2 |
| #26011888 | 2 |
| #26011887 | 2 |
| #106×D173 | 2 |
| C4×C8×D173 | 2 |
| #498×C173 | 2 |
| C2×#498 | 173 |