Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #26041907 | C2 | semidirect |
| 3. #26041644 | C2 | semidirect |
| 4. #26041639 | C2 | semidirect |
| 5. #26041634 | C2 | semidirect |
| 6. #26041626 | C2 | semidirect |
| 7. #26041285 | C2 | semidirect |
| 8. #26041281 | C2 | semidirect |
| 9. #26041276 | C2 | semidirect |
| 10. C2×#19153738 | C2 | semidirect |
| 11. #405×C181 | C2 | semidirect |
| 14. #19153816 | C22 | semidirect |
| 17. #19153808 | C22 | semidirect |
| 26. #19153741 | C22 | semidirect |
| 27. #19153741 | C22 | semidirect |
| 28. #19153741 | C22 | semidirect |
| 33. #19153738 | C22 | semidirect |
| 34. #19153738 | C22 | semidirect |
| 35. #19153738 | C22 | semidirect |
| 39. #97×C181 | C22 | semidirect |
| 40. C4×C8×C181 | C22 | semidirect |
| 135. C181 | #3136 | semidirect |
| 147. #405 | D181 | semidirect |
| 175. #97 | C2×D181 | semidirect |
| 176. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041907 | 2 |
| #26041848 | 2 |
| #26041644 | 2 |
| #26041639 | 2 |
| #26041634 | 2 |
| #26041626 | 2 |
| #26041285 | 2 |
| #26041281 | 2 |
| #26041276 | 2 |
| C2×#19153738 | 2 |
| #405×C181 | 2 |
| #3136 | 181 |