Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041836 | C2 | semidirect |
| 3. #26041621 | C2 | semidirect |
| 4. #26041575 | C2 | semidirect |
| 5. #26041570 | C2 | semidirect |
| 6. #26041490 | C2 | semidirect |
| 7. #26041485 | C2 | semidirect |
| 9. #26041387 | C2 | semidirect |
| 10. #26041381 | C2 | semidirect |
| 11. #432×C181 | C2 | semidirect |
| 136. C181 | #3116 | semidirect |
| 148. #432 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041836 | 2 |
| C4×#15668449 | 2 |
| #26041621 | 2 |
| #26041575 | 2 |
| #26041570 | 2 |
| #26041490 | 2 |
| #26041485 | 2 |
| #26041443 | 2 |
| #26041387 | 2 |
| #26041381 | 2 |
| #432×C181 | 2 |
| #3116 | 181 |