Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
260 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 64 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⋊M32 | C2 | semidirect |
| 2. #26042289 | C2 | semidirect |
| 3. #26042191 | C2 | semidirect |
| 8. D181⋊C16 | C22 | semidirect |
| 9. #19153885 | C22 | semidirect |
| 12. C2×D1448 | C4 | semidirect |
| 16. D8×D181 | C4 | semidirect |
| 19. C2×D8×C181 | C4 | semidirect |
| 89. C181 | #2140 | semidirect |
| 102. C2×D8 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊M32 | 2 |
| #26042289 | 2 |
| #26042191 | 2 |
| C2×D8×D181 | 2 |
| #2140 | 181 |