Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 565 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. C23×Dic346 | C2 | semidirect |
| 2. C2×#19149709 | C2 | direct (N × H) |
| 3. C22×#14583816 | C2 | semidirect |
| 4. C22×#14583814 | C2 | semidirect |
| 5. C22×#14583810 | C2 | semidirect |
| 10. C22×Dic346 | C22 | semidirect |
| 12. #19149709 | C22 | direct (N × H) |
| 13. C2×#14583816 | C22 | semidirect |
| 14. C2×#14583814 | C22 | semidirect |
| 15. C2×#14583810 | C22 | semidirect |
| 28. C2×Dic346 | C23 | semidirect |
| 31. #14583816 | C23 | semidirect |
| 32. #14583814 | C23 | semidirect |
| 33. #14583810 | C23 | semidirect |
| 76. C22×C173 | #137 | semidirect |
| 86. C2×C173 | C2×#137 | semidirect |
| 88. C173 | C22×#137 | semidirect |
| 165. C22 | #19149709 | direct (N × H) |
| 175. C2 | C2×#19149709 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic346 | 2 |
| C2×#19149709 | 2 |
| C22×#14583816 | 2 |
| C22×#14583814 | 2 |
| C22×#14583810 | 2 |
| C22×#41×C173 | 2 |
| C22×#137 | 173 |