Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26041830 | C2 | semidirect |
| 2. C4×D4×D181 | C2 | semidirect |
| 3. #26041594 | C2 | semidirect |
| 4. #26041556 | C2 | semidirect |
| 5. #26041475 | C2 | semidirect |
| 6. #26041474 | C2 | semidirect |
| 7. #26041414 | C2 | semidirect |
| 8. #26041361 | C2 | semidirect |
| 9. #26041359 | C2 | semidirect |
| 10. #26041331 | C2 | semidirect |
| 11. #474×C181 | C2 | semidirect |
| 17. #19153813 | C22 | semidirect |
| 25. #19153778 | C22 | semidirect |
| 31. #19153749 | C22 | semidirect |
| 32. C4⋊#13089678 | C22 | semidirect |
| 33. #19153738 | C22 | semidirect |
| 35. #19153736 | C22 | semidirect |
| 37. C8×Dic181 | C22 | semidirect |
| 38. C4⋊Q8×C181 | C22 | semidirect |
| 40. #107×C181 | C22 | semidirect |
| 41. C4⋊C8×C181 | C22 | semidirect |
| 96. D724 | #41 | semidirect |
| 110. C4×D181 | D8 | semidirect |
| 115. D4×C181 | #41 | semidirect |
| 154. C181 | #3100 | semidirect |
| 160. #474 | D181 | semidirect |
| 172. C4⋊Q8 | C2×D181 | semidirect |
| 189. #107 | C2×D181 | semidirect |
| 191. C4⋊C8 | C2×D181 | semidirect |
| 256. D4 | #15668450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041830 | 2 |
| C4×D4×D181 | 2 |
| #26041594 | 2 |
| #26041556 | 2 |
| #26041475 | 2 |
| #26041474 | 2 |
| #26041414 | 2 |
| #26041361 | 2 |
| #26041359 | 2 |
| #26041331 | 2 |
| #474×C181 | 2 |
| #3100 | 181 |