Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1144 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 309 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. #26041141 | C2 | direct (N × H) |
| 4. C2×#19153723 | C2 | semidirect |
| 5. C2×#19153723 | C2 | semidirect |
| 6. C2×#95×C181 | C2 | semidirect |
| 11. C22×C4×D181 | C4 | semidirect |
| 15. #19153723 | C22 | semidirect |
| 16. #19153723 | C22 | semidirect |
| 19. #95×C181 | C22 | semidirect |
| 35. C2×C4×D181 | C2×C4 | semidirect |
| 96. C2×C181 | #381 | semidirect |
| 103. C181 | C2×#381 | semidirect |
| 110. C2×#95 | D181 | semidirect |
| 123. #95 | C2×D181 | semidirect |
| 201. C2 | #26041141 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D181 | 2 |
| C22×#15668426 | 2 |
| #26041141 | 2 |
| C2×#19153723 | 2 |
| C2×#95×C181 | 2 |
| C2×#381 | 181 |