Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
760 conjugacy classes of subgroups; only the 498 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 498 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×#13089685 | C2 | direct (N × H) |
| 4. C22×#13089685 | C4 | direct (N × H) |
| 6. C4×#13089685 | C22 | direct (N × H) |
| 12. C2×#13089685 | C2×C4 | direct (N × H) |
| 14. C22×Dic181 | C8 | semidirect |
| 22. C22×C4×C181 | C8 | semidirect |
| 24. #13089685 | C22×C4 | direct (N × H) |
| 26. C2×Dic181 | C2×C8 | semidirect |
| 35. C2×C4×C181 | C2×C8 | semidirect |
| 37. C22×C181 | C4×C8 | semidirect |
| 42. C4×C181 | C22×C8 | semidirect |
| 44. Dic181 | C22×C8 | semidirect |
| 46. C2×C181 | C2×C4×C8 | semidirect |
| 50. C181 | C22×C4×C8 | semidirect |
| 69. C22×C4 | #13089685 | direct (N × H) |
| 85. C2×C4 | C2×#13089685 | direct (N × H) |
| 88. C22 | C4×#13089685 | direct (N × H) |
| 96. C4 | C22×#13089685 | direct (N × H) |
| 97. C2 | C2×C4×#13089685 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13089685 | 2 |
| C2×C4×#13089685 | 2 |
| C22×C4×Dic181 | 2 |
| C22×C4×C8 | 181 |