Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19153838 | C2 | semidirect |
| 2. C22×#15668432 | C2 | semidirect |
| 3. #26041791 | C2 | semidirect |
| 4. #26041538 | C2 | semidirect |
| 5. #26041533 | C2 | semidirect |
| 6. #26041526 | C2 | semidirect |
| 7. #26041273 | C2 | semidirect |
| 8. #427×C181 | C2 | semidirect |
| 12. C2×Dic724 | C22 | semidirect |
| 13. C2×#15668438 | C22 | semidirect |
| 14. C2×D1448 | C22 | semidirect |
| 24. #19153739 | C22 | semidirect |
| 25. #19153736 | C22 | semidirect |
| 28. #107×C181 | C22 | semidirect |
| 29. #106×C181 | C22 | semidirect |
| 54. C2×C8×C181 | D4 | semidirect |
| 105. C181 | #3054 | semidirect |
| 113. #427 | D181 | semidirect |
| 132. #107 | C2×D181 | semidirect |
| 133. #106 | C2×D181 | semidirect |
| 157. C2×C8 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153838 | 2 |
| C22×#15668432 | 2 |
| #26041791 | 2 |
| #26041538 | 2 |
| #26041533 | 2 |
| #26041526 | 2 |
| #26041273 | 2 |
| #427×C181 | 2 |
| #3054 | 181 |