Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19149707 | C2 | semidirect |
| 2. C2×#19149676 | C2 | semidirect |
| 3. C4×#14583826 | C2 | semidirect |
| 4. #26011692 | C2 | semidirect |
| 5. #26011687 | C2 | semidirect |
| 6. #26011497 | C2 | semidirect |
| 7. #423×C173 | C2 | semidirect |
| 12. C2×#14583815 | C22 | semidirect |
| 13. C2×D1384 | C22 | semidirect |
| 17. C4×Dic346 | C22 | semidirect |
| 18. C4×D692 | C22 | semidirect |
| 23. #19149601 | C22 | semidirect |
| 26. C4⋊C8×C173 | C22 | semidirect |
| 29. #14583826 | D4 | semidirect |
| 62. Dic346 | C2×D4 | semidirect |
| 69. D692 | C2×D4 | semidirect |
| 94. C4×C173 | AGL(1,ℤ/8) | semidirect |
| 104. C173 | #3038 | semidirect |
| 111. #423 | D173 | semidirect |
| 130. C4⋊C8 | C2×D173 | semidirect |
| 201. C4 | #19149707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149707 | 2 |
| C2×#19149676 | 2 |
| C4×#14583826 | 2 |
| #26011692 | 2 |
| #26011687 | 2 |
| #26011497 | 2 |
| #423×C173 | 2 |
| #3038 | 173 |