Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #26041990 | C2 | semidirect |
| 3. #26041622 | C2 | semidirect |
| 4. #26041594 | C2 | semidirect |
| 5. #26041571 | C2 | semidirect |
| 6. #26041566 | C2 | semidirect |
| 7. #26041526 | C2 | semidirect |
| 8. C4×#15668438 | C2 | semidirect |
| 9. #26041358 | C2 | semidirect |
| 10. #26041320 | C2 | semidirect |
| 11. #500×C181 | C2 | semidirect |
| 121. C181 | #3357 | semidirect |
| 125. #500 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041995 | 2 |
| #26041990 | 2 |
| #26041622 | 2 |
| #26041594 | 2 |
| #26041571 | 2 |
| #26041566 | 2 |
| #26041526 | 2 |
| C4×#15668438 | 2 |
| #26041358 | 2 |
| #26041320 | 2 |
| #500×C181 | 2 |
| #3357 | 181 |