Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
346 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 1. #26011966 | C2 | semidirect |
| 2. #26011508 | C2 | semidirect |
| 3. #26011496 | C2 | semidirect |
| 4. #26011465 | C2 | semidirect |
| 5. #26011262 | C2 | semidirect |
| 6. #26011248 | C2 | semidirect |
| 22. C2×SD16×C173 | C4 | semidirect |
| 23. C2×D8×C173 | C4 | semidirect |
| 44. C2×Q8×C173 | C2×C4 | semidirect |
| 50. C2×D4×C173 | C2×C4 | semidirect |
| 59. C2×C8×C173 | C2×C4 | semidirect |
| 115. C173 | #1904 | semidirect |
| 128. C2×SD16 | Dic173 | semidirect |
| 129. C2×D8 | Dic173 | semidirect |
| 146. C2×Q8 | C2×Dic173 | semidirect |
| 152. C2×D4 | C2×Dic173 | semidirect |
| 165. C2×C8 | C2×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011966 | 2 |
| #26011508 | 2 |
| #26011496 | 2 |
| #26011465 | 2 |
| #26011262 | 2 |
| #26011248 | 2 |
| C2×AGL(1,ℤ/8)×C173 | 2 |
| #1904 | 173 |