Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
458 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 2. C2×C4⋊C4×D181 | C2 | semidirect |
| 3. #26041613 | C2 | semidirect |
| 4. #26041608 | C2 | semidirect |
| 5. #26041596 | C2 | semidirect |
| 6. #26041591 | C2 | semidirect |
| 7. #26041321 | C2 | semidirect |
| 8. #26041319 | C2 | semidirect |
| 9. #26041280 | C2 | semidirect |
| 10. #26041242 | C2 | semidirect |
| 11. #417×C181 | C2 | semidirect |
| 30. #19153750 | C22 | semidirect |
| 31. #19153749 | C22 | semidirect |
| 32. #19153748 | C22 | semidirect |
| 33. #19153747 | C22 | semidirect |
| 34. #19153740 | C22 | semidirect |
| 35. #19153737 | C22 | semidirect |
| 41. #103×C181 | C22 | semidirect |
| 42. #102×C181 | C22 | semidirect |
| 155. C181 | #3092 | semidirect |
| 166. #417 | D181 | semidirect |
| 194. #103 | C2×D181 | semidirect |
| 196. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041786 | 2 |
| C2×C4⋊C4×D181 | 2 |
| #26041613 | 2 |
| #26041608 | 2 |
| #26041596 | 2 |
| #26041591 | 2 |
| #26041321 | 2 |
| #26041319 | 2 |
| #26041280 | 2 |
| #26041242 | 2 |
| #417×C181 | 2 |
| #3092 | 181 |