Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
196 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. #26042166 | C2 | semidirect |
| 4. C16×#10624382 | C2 | semidirect |
| 8. #19153891 | C4 | semidirect |
| 9. #19153890 | C4 | semidirect |
| 16. #19153756 | C4 | semidirect |
| 17. #19153755 | C4 | semidirect |
| 19. M32×C181 | C4 | semidirect |
| 28. #15668452 | C2×C4 | semidirect |
| 35. #15668424 | C2×C4 | semidirect |
| 37. C16×C181 | C2×C4 | semidirect |
| 59. #10624382 | M32 | direct (N × H) |
| 68. C181 | C4×M32 | semidirect |
| 82. M32 | #10624382 | direct (N × H) |
| 106. C16 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊M32 | 2 |
| C2×C8×#10624382 | 2 |
| #26042166 | 2 |
| C16×#10624382 | 2 |
| M32×D181 | 2 |
| C4×M32 | 181 |