Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26041760 | C2 | semidirect |
| 5. #26041500 | C2 | semidirect |
| 6. #26041493 | C2 | semidirect |
| 7. #26041488 | C2 | semidirect |
| 8. #26041483 | C2 | semidirect |
| 9. #26041307 | C2 | semidirect |
| 10. C2×#19153739 | C2 | semidirect |
| 11. #417×C181 | C2 | semidirect |
| 146. C181 | #3046 | semidirect |
| 157. #417 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| C2×#19153836 | 2 |
| #26041850 | 2 |
| #26041760 | 2 |
| #26041500 | 2 |
| #26041493 | 2 |
| #26041488 | 2 |
| #26041483 | 2 |
| #26041307 | 2 |
| C2×#19153739 | 2 |
| #417×C181 | 2 |
| #3046 | 181 |