Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
272 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×C16×D173 | C2 | semidirect |
| 3. #107×D173 | C2 | semidirect |
| 4. #26011293 | C2 | semidirect |
| 5. #26011292 | C2 | semidirect |
| 6. #26011291 | C2 | semidirect |
| 7. #357×C173 | C2 | semidirect |
| 12. D8×D173 | C4 | semidirect |
| 15. C2×#14583801 | C22 | semidirect |
| 17. #19149613 | C22 | semidirect |
| 20. C2×C16×C173 | C22 | semidirect |
| 21. #107×C173 | C22 | semidirect |
| 30. D1384 | C2×C4 | semidirect |
| 40. D8×C173 | C2×C4 | semidirect |
| 86. D173 | #357 | direct (N × H) |
| 87. C173 | C2×#357 | semidirect |
| 95. #357 | D173 | direct (N × H) |
| 106. C2×C16 | C2×D173 | semidirect |
| 109. #107 | C2×D173 | semidirect |
| 122. D8 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D173 | 2 |
| C2×C16×D173 | 2 |
| #107×D173 | 2 |
| #26011293 | 2 |
| #26011292 | 2 |
| #26011291 | 2 |
| #357×C173 | 2 |
| C2×#357 | 173 |