Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041884 | C2 | semidirect |
| 2. #26041848 | C2 | semidirect |
| 3. #26041668 | C2 | semidirect |
| 4. #26041656 | C2 | semidirect |
| 5. #26041644 | C2 | semidirect |
| 6. #26041634 | C2 | semidirect |
| 7. #26041495 | C2 | semidirect |
| 8. #26041475 | C2 | semidirect |
| 9. #26041426 | C2 | semidirect |
| 10. #26041415 | C2 | semidirect |
| 11. #433×C181 | C2 | semidirect |
| 14. C2×#15668438 | C22 | semidirect |
| 17. C2×D1448 | C22 | semidirect |
| 20. #19153813 | C22 | semidirect |
| 21. #19153808 | C22 | semidirect |
| 29. C4×D724 | C22 | semidirect |
| 30. #19153741 | C22 | semidirect |
| 33. #19153738 | C22 | semidirect |
| 35. C4⋊C8×C181 | C22 | semidirect |
| 37. #97×C181 | C22 | semidirect |
| 38. C4×C8×C181 | C22 | semidirect |
| 128. C181 | #3220 | semidirect |
| 140. #433 | D181 | semidirect |
| 160. C4⋊C8 | C2×D181 | semidirect |
| 166. #97 | C2×D181 | semidirect |
| 167. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041884 | 2 |
| #26041848 | 2 |
| #26041668 | 2 |
| #26041656 | 2 |
| #26041644 | 2 |
| #26041634 | 2 |
| #26041495 | 2 |
| #26041475 | 2 |
| #26041426 | 2 |
| #26041415 | 2 |
| #433×C181 | 2 |
| #3220 | 181 |