Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
184 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
| 14. C2×#15668424 | C4 | semidirect |
| 15. C16×D181 | C4 | semidirect |
| 16. C16×D181 | C4 | semidirect |
| 19. C2×C16×C181 | C4 | semidirect |
| 64. C181 | #2108 | semidirect |
| 82. C2×C16 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊M32 | 2 |
| #26042242 | 2 |
| #26042166 | 2 |
| C16×#10624382 | 2 |
| C2×C16×D181 | 2 |
| #2108 | 181 |