Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
616 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 616 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×D4×Dic181 | C2 | semidirect |
| 3. C2×#19153778 | C2 | semidirect |
| 4. #26041359 | C2 | direct (N × H) |
| 5. C2×#19153749 | C2 | semidirect |
| 6. C2×#19153738 | C2 | semidirect |
| 7. C2×C8×Dic181 | C2 | semidirect |
| 8. C2×#102×C181 | C2 | semidirect |
| 12. C2×#15668434 | C4 | semidirect |
| 16. D4×Dic181 | C22 | semidirect |
| 18. #19153778 | C22 | semidirect |
| 23. #19153749 | C22 | semidirect |
| 24. #19153738 | C22 | semidirect |
| 25. C8×Dic181 | C22 | semidirect |
| 29. #102×C181 | C22 | semidirect |
| 33. C2×D724 | C2×C4 | semidirect |
| 42. #15668434 | C2×C4 | semidirect |
| 43. C2×#13089678 | C2×C4 | semidirect |
| 54. C2×D4×C181 | C2×C4 | semidirect |
| 68. D724 | C22×C4 | semidirect |
| 73. C2×Dic181 | D8 | semidirect |
| 77. #13089678 | C22×C4 | semidirect |
| 85. D4×C181 | C22×C4 | semidirect |
| 111. Dic181 | C2×D8 | semidirect |
| 113. C2×C181 | C4×D8 | semidirect |
| 118. C181 | C2×C4×D8 | semidirect |
| 126. C2×#102 | D181 | semidirect |
| 147. #102 | C2×D181 | semidirect |
| 157. C2×D4 | C4×D181 | semidirect |
| 195. D4 | C2×C4×D181 | semidirect |
| 233. C2 | #26041359 | 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×D4×Dic181 | 2 |
| C2×#19153778 | 2 |
| #26041359 | 2 |
| C2×#19153749 | 2 |
| C2×#19153738 | 2 |
| C2×C8×Dic181 | 2 |
| C2×#102×C181 | 2 |
| C2×C4×D8 | 181 |