Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 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. D181⋊#108 | C2 | semidirect |
| 2. C2×#19153884 | C2 | semidirect |
| 4. #26042158 | C2 | semidirect |
| 16. #19153824 | C4 | semidirect |
| 17. #19153823 | C4 | semidirect |
| 19. #19153822 | C4 | semidirect |
| 24. #131×C181 | C4 | semidirect |
| 112. C181 | #1815 | semidirect |
| 125. #131 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊#108 | 2 |
| C2×#19153884 | 2 |
| #26042270 | 2 |
| #26042158 | 2 |
| #131×D181 | 2 |
| #1815 | 181 |