Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
436 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 1. C2×#19153878 | C2 | semidirect |
| 2. C4×D181⋊C8 | C2 | semidirect |
| 3. #26042225 | C2 | semidirect |
| 12. #19153813 | C4 | semidirect |
| 14. #19153812 | C4 | semidirect |
| 16. #127×C181 | C4 | semidirect |
| 19. D181⋊C8 | D4 | semidirect |
| 76. C4×C181 | #102 | semidirect |
| 78. Dic181 | #102 | semidirect |
| 87. C181 | #1957 | semidirect |
| 99. #127 | #10624382 | semidirect |
| 166. C4 | #19153878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153878 | 2 |
| C4×D181⋊C8 | 2 |
| #26042225 | 2 |
| #127×D181 | 2 |
| #1957 | 181 |