Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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×Dic362 | C2 | semidirect |
| 3. C4×#15668437 | C2 | direct (N × H) |
| 4. C2×#19153747 | C2 | semidirect |
| 5. C2×#19153739 | C2 | semidirect |
| 7. C2×C4×#13089678 | C2 | semidirect |
| 10. C2×#15668437 | C4 | direct (N × H) |
| 15. C4×Dic362 | C22 | semidirect |
| 19. #19153747 | C22 | semidirect |
| 20. #19153739 | C22 | semidirect |
| 22. C4×#13089678 | C22 | semidirect |
| 32. C2×Dic362 | C2×C4 | semidirect |
| 36. #15668437 | C2×C4 | direct (N × H) |
| 38. C2×#13089678 | C2×C4 | semidirect |
| 63. Dic362 | C22×C4 | semidirect |
| 69. #13089678 | C22×C4 | semidirect |
| 82. C2×C4×C181 | SD16 | semidirect |
| 100. C4×C181 | C2×SD16 | semidirect |
| 106. C2×C181 | C4×SD16 | semidirect |
| 110. C181 | C2×C4×SD16 | semidirect |
| 191. C2×C4 | #15668437 | direct (N × H) |
| 213. C4 | C2×#15668437 | direct (N × H) |
| 217. C2 | C4×#15668437 | 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×C4×Dic362 | 2 |
| C4×#15668437 | 2 |
| C2×#19153747 | 2 |
| C2×#19153739 | 2 |
| C2×#19153737 | 2 |
| C2×C4×#13089678 | 2 |
| C2×C4×D4×C181 | 2 |
| C2×C4×SD16 | 181 |