Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #26041621 | C2 | semidirect |
| 4. #26041615 | C2 | semidirect |
| 5. #26041610 | C2 | semidirect |
| 6. #26041321 | C2 | semidirect |
| 7. #26041289 | C2 | semidirect |
| 25. #19153750 | C22 | semidirect |
| 26. #19153748 | C22 | semidirect |
| 27. #19153741 | C22 | semidirect |
| 28. #19153741 | C22 | semidirect |
| 116. C181 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153795 | 2 |
| C2×#19153775 | 2 |
| #26041621 | 2 |
| #26041615 | 2 |
| #26041610 | 2 |
| #26041321 | 2 |
| #26041289 | 2 |
| #407×C181 | 2 |
| #3095 | 181 |