Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
196 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26011556 | C2 | semidirect |
| 3. #26011218 | C2 | semidirect |
| 4. C8×#13063436 | C2 | semidirect |
| 5. #335×C173 | C2 | semidirect |
| 18. D1384 | C8 | semidirect |
| 31. D692 | C2×C8 | semidirect |
| 37. #13063436 | D8 | semidirect |
| 43. C8×C173 | C2×C8 | semidirect |
| 58. C173 | C8×D8 | semidirect |
| 62. #335 | D173 | semidirect |
| 102. C8 | C8×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1384 | 2 |
| #26011556 | 2 |
| #26011218 | 2 |
| C8×#13063436 | 2 |
| #335×C173 | 2 |
| C8×D8 | 173 |