Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19153847 | C2 | semidirect |
| 2. C2×#19153841 | C2 | semidirect |
| 3. C2×#19153836 | C2 | semidirect |
| 4. C22×#15668436 | C2 | semidirect |
| 5. #26041848 | C2 | semidirect |
| 6. #26041671 | C2 | semidirect |
| 7. #26041669 | C2 | semidirect |
| 8. #26041661 | C2 | semidirect |
| 9. #26041653 | C2 | semidirect |
| 10. #26041235 | C2 | semidirect |
| 11. #536×C181 | C2 | semidirect |
| 17. C2×#15668439 | C22 | semidirect |
| 18. C2×#15668439 | C22 | semidirect |
| 19. C2×#15668437 | C22 | semidirect |
| 24. C2×#15668436 | C22 | semidirect |
| 25. C2×#15668436 | C22 | semidirect |
| 27. C2×#15668434 | C22 | semidirect |
| 34. #19153727 | C22 | semidirect |
| 35. C4×#13089678 | C22 | semidirect |
| 38. C4⋊Q8×C181 | C22 | semidirect |
| 39. #124×C181 | C22 | semidirect |
| 65. #15668433 | D4 | semidirect |
| 66. C2×#13089678 | D4 | semidirect |
| 148. C181 | #3154 | semidirect |
| 154. #536 | D181 | semidirect |
| 181. C4⋊Q8 | C2×D181 | semidirect |
| 184. #124 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153847 | 2 |
| C2×#19153841 | 2 |
| C2×#19153836 | 2 |
| C22×#15668436 | 2 |
| #26041848 | 2 |
| #26041671 | 2 |
| #26041669 | 2 |
| #26041661 | 2 |
| #26041653 | 2 |
| #26041235 | 2 |
| #536×C181 | 2 |
| #3154 | 181 |