Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1296 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 565 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. #26041905 | C2 | direct (N × H) |
| 2. C2×#19153795 | C2 | semidirect |
| 3. C2×#19153793 | C2 | semidirect |
| 6. C22×Dic362 | C22 | semidirect |
| 8. #19153795 | C22 | semidirect |
| 9. #19153793 | C22 | semidirect |
| 10. C2×C4⋊Dic181 | C22 | semidirect |
| 11. C2×#15668428 | C22 | semidirect |
| 20. C2×Dic362 | C23 | semidirect |
| 24. C4⋊Dic181 | C23 | semidirect |
| 25. #15668428 | C23 | semidirect |
| 29. C24×C181 | Q8 | semidirect |
| 47. C23×C181 | C2×Q8 | semidirect |
| 68. C2×C181 | #543 | semidirect |
| 71. C181 | C2×#543 | semidirect |
| 92. C24 | Dic362 | semidirect |
| 115. C23 | C2×Dic362 | semidirect |
| 140. C2 | #26041905 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041905 | 2 |
| C2×#19153795 | 2 |
| C2×#19153793 | 2 |
| C22×C22⋊Dic181 | 2 |
| C22×C22⋊C4×C181 | 2 |
| C2×#543 | 181 |