Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 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×#19153849 | C2 | semidirect |
| 3. #26041850 | C2 | semidirect |
| 4. #26041537 | C2 | semidirect |
| 5. #26041525 | C2 | semidirect |
| 6. #26041520 | C2 | semidirect |
| 7. #26041508 | C2 | semidirect |
| 8. #26041321 | C2 | semidirect |
| 9. #26041276 | C2 | semidirect |
| 10. C2×#19153741 | C2 | semidirect |
| 11. C2×#131×C181 | C2 | semidirect |
| 79. M16×C181 | D4 | semidirect |
| 143. C181 | #3063 | semidirect |
| 146. C2×#131 | D181 | semidirect |
| 210. M16 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| #26041857 | 2 |
| #26041850 | 2 |
| #26041537 | 2 |
| #26041525 | 2 |
| #26041520 | 2 |
| #26041508 | 2 |
| #26041321 | 2 |
| #26041276 | 2 |
| C2×#19153741 | 2 |
| C2×#131×C181 | 2 |
| #3063 | 181 |