Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#19153843 | C2 | semidirect |
| 2. #26041830 | C2 | semidirect |
| 3. C4×D4×D181 | C2 | semidirect |
| 4. #26041497 | C2 | semidirect |
| 5. #26041496 | C2 | semidirect |
| 6. #26041481 | C2 | semidirect |
| 7. #26041475 | C2 | semidirect |
| 8. #26041474 | C2 | semidirect |
| 9. #26041301 | C2 | semidirect |
| 10. #26041279 | C2 | semidirect |
| 11. #461×C181 | C2 | semidirect |
| 20. #19153813 | C22 | semidirect |
| 21. #19153805 | C22 | semidirect |
| 34. C4⋊#13089678 | C22 | semidirect |
| 35. #19153745 | C22 | semidirect |
| 36. #19153740 | C22 | semidirect |
| 37. #19153738 | C22 | semidirect |
| 38. #19153736 | C22 | semidirect |
| 40. C4⋊Q8×C181 | C22 | semidirect |
| 42. C4⋊C8×C181 | C22 | semidirect |
| 43. #103×C181 | C22 | semidirect |
| 54. D4×D181 | D4 | semidirect |
| 146. C4×C181 | AGL(1,ℤ/8) | semidirect |
| 160. C181 | #3036 | semidirect |
| 168. #461 | D181 | semidirect |
| 182. C4⋊Q8 | C2×D181 | semidirect |
| 200. C4⋊C8 | C2×D181 | semidirect |
| 202. #103 | C2×D181 | semidirect |
| 311. C4 | #19153843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153843 | 2 |
| #26041830 | 2 |
| C4×D4×D181 | 2 |
| #26041497 | 2 |
| #26041496 | 2 |
| #26041481 | 2 |
| #26041475 | 2 |
| #26041474 | 2 |
| #26041301 | 2 |
| #26041279 | 2 |
| #461×C181 | 2 |
| #3036 | 181 |