Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
300 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 4. #26041234 | C2 | semidirect |
| 5. #26041044 | C2 | semidirect |
| 6. #26041039 | C2 | semidirect |
| 7. C2×C4×C8×C181 | C2 | semidirect |
| 10. #19153822 | C4 | semidirect |
| 16. #19153744 | C4 | semidirect |
| 17. #19153741 | C4 | semidirect |
| 18. #19153738 | C4 | semidirect |
| 98. C181 | #1764 | semidirect |
| 104. C2×C4×C8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153822 | 2 |
| C2×#19153744 | 2 |
| #26041276 | 2 |
| #26041234 | 2 |
| #26041044 | 2 |
| #26041039 | 2 |
| C2×C4×C8×C181 | 2 |
| #1764 | 181 |