Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
552 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 552 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×#19153781 | C2 | semidirect |
| 4. #26041370 | C2 | direct (N × H) |
| 5. C2×#19153747 | C2 | semidirect |
| 6. C2×#19153741 | C2 | semidirect |
| 7. C2×C8×Dic181 | C2 | semidirect |
| 11. C2×#15668437 | C4 | semidirect |
| 15. #19153781 | C22 | semidirect |
| 23. #19153747 | C22 | semidirect |
| 24. #19153741 | C22 | semidirect |
| 25. C8×Dic181 | C22 | semidirect |
| 32. C2×Dic362 | C2×C4 | semidirect |
| 40. #15668437 | C2×C4 | semidirect |
| 41. C2×#13089678 | C2×C4 | semidirect |
| 63. Dic362 | C22×C4 | semidirect |
| 70. C2×Dic181 | SD16 | semidirect |
| 73. #13089678 | C22×C4 | semidirect |
| 104. Dic181 | C2×SD16 | semidirect |
| 106. C2×C181 | C4×SD16 | semidirect |
| 110. C181 | C2×C4×SD16 | semidirect |
| 217. C2 | #26041370 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668437 | 2 |
| C2×#19153781 | 2 |
| C2×D4×Dic181 | 2 |
| #26041370 | 2 |
| C2×#19153747 | 2 |
| C2×#19153741 | 2 |
| C2×C8×Dic181 | 2 |
| C2×#102×C181 | 2 |
| C2×C4×SD16 | 181 |