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. #26041827 | C2 | semidirect |
| 2. C4×D4×D181 | C2 | semidirect |
| 3. #26041591 | C2 | semidirect |
| 4. #26041560 | C2 | semidirect |
| 5. #26041559 | C2 | semidirect |
| 6. #26041471 | C2 | semidirect |
| 7. #26041411 | C2 | semidirect |
| 8. D8×Dic181 | C2 | semidirect |
| 9. #26041359 | C2 | semidirect |
| 10. #26041331 | C2 | semidirect |
| 11. #459×C181 | C2 | semidirect |
| 16. #19153816 | C22 | semidirect |
| 23. D4×Dic181 | C22 | semidirect |
| 30. #19153750 | C22 | semidirect |
| 31. #19153749 | C22 | semidirect |
| 32. C4⋊#13089678 | C22 | semidirect |
| 35. #19153737 | C22 | semidirect |
| 37. C8×Dic181 | C22 | semidirect |
| 39. #127×C181 | C22 | semidirect |
| 41. C4⋊C8×C181 | C22 | semidirect |
| 42. #102×C181 | C22 | semidirect |
| 91. D724 | #41 | semidirect |
| 107. C4×D181 | D8 | semidirect |
| 116. D4×C181 | #41 | semidirect |
| 154. C181 | #3100 | semidirect |
| 162. #459 | D181 | semidirect |
| 173. #127 | C2×D181 | semidirect |
| 191. C4⋊C8 | C2×D181 | semidirect |
| 195. #102 | C2×D181 | semidirect |
| 256. D4 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041827 | 2 |
| C4×D4×D181 | 2 |
| #26041591 | 2 |
| #26041560 | 2 |
| #26041559 | 2 |
| #26041471 | 2 |
| #26041411 | 2 |
| D8×Dic181 | 2 |
| #26041359 | 2 |
| #26041331 | 2 |
| #459×C181 | 2 |
| #3100 | 181 |