Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 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 |
|---|---|---|
| 1. #26042092 | C2 | semidirect |
| 2. #26042085 | C2 | semidirect |
| 3. #26042080 | C2 | semidirect |
| 4. #26041551 | C2 | semidirect |
| 5. #26041546 | C2 | semidirect |
| 6. #26041539 | C2 | semidirect |
| 7. #26041456 | C2 | semidirect |
| 8. #26041451 | C2 | semidirect |
| 9. #26041397 | C2 | semidirect |
| 10. #26041397 | C2 | semidirect |
| 11. #495×C181 | C2 | semidirect |
| 12. #19153864 | C22 | semidirect |
| 16. #19153847 | C22 | semidirect |
| 20. #19153842 | C22 | semidirect |
| 31. #19153822 | C22 | semidirect |
| 32. #19153822 | C22 | semidirect |
| 33. #19153752 | C22 | semidirect |
| 34. #19153752 | C22 | semidirect |
| 36. #19153744 | C22 | semidirect |
| 37. #19153744 | C22 | semidirect |
| 38. #19153735 | C22 | semidirect |
| 39. #19153733 | C22 | semidirect |
| 40. C2×Q16×C181 | C22 | semidirect |
| 41. C2×SD16×C181 | C22 | semidirect |
| 43. #124×C181 | C22 | semidirect |
| 44. C4×C8×C181 | C22 | semidirect |
| 149. C181 | #3290 | semidirect |
| 154. #495 | D181 | semidirect |
| 178. C2×Q16 | C2×D181 | semidirect |
| 180. C2×SD16 | C2×D181 | semidirect |
| 186. #124 | C2×D181 | semidirect |
| 194. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042092 | 2 |
| #26042085 | 2 |
| #26042080 | 2 |
| #26041551 | 2 |
| #26041546 | 2 |
| #26041539 | 2 |
| #26041456 | 2 |
| #26041451 | 2 |
| #26041397 | 2 |
| #495×C181 | 2 |
| #3290 | 181 |