Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
608 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 205 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×D724 | C2 | semidirect |
| 3. #26041389 | C2 | direct (N × H) |
| 4. C2×#19153747 | C2 | semidirect |
| 5. C2×#19153737 | C2 | semidirect |
| 6. C2×#19153736 | C2 | semidirect |
| 7. C2×#19153727 | C2 | semidirect |
| 8. C2×C4×D4×C181 | C2 | semidirect |
| 11. C2×#15668434 | C4 | semidirect |
| 16. C4×D724 | C22 | semidirect |
| 19. #19153747 | C22 | semidirect |
| 20. #19153737 | C22 | semidirect |
| 21. #19153736 | C22 | semidirect |
| 22. #19153727 | C22 | semidirect |
| 26. C4×D4×C181 | C22 | semidirect |
| 33. C2×D724 | C2×C4 | semidirect |
| 38. #15668434 | C2×C4 | semidirect |
| 40. C2×#13089678 | C2×C4 | semidirect |
| 49. C2×D4×C181 | C2×C4 | semidirect |
| 68. D724 | C22×C4 | semidirect |
| 73. #13089678 | C22×C4 | semidirect |
| 81. D4×C181 | C22×C4 | semidirect |
| 113. C2×C181 | #442 | semidirect |
| 118. C181 | C2×#442 | semidirect |
| 122. C2×C4×D4 | D181 | semidirect |
| 139. C4×D4 | C2×D181 | semidirect |
| 157. C2×D4 | C4×D181 | semidirect |
| 195. D4 | C2×C4×D181 | semidirect |
| 233. C2 | #26041389 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668434 | 2 |
| C2×C4×D724 | 2 |
| #26041389 | 2 |
| C2×#19153747 | 2 |
| C2×#19153737 | 2 |
| C2×#19153736 | 2 |
| C2×#19153727 | 2 |
| C2×C4×D4×C181 | 2 |
| C2×#442 | 181 |