Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
3464 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 429 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 |
|---|---|---|
| 2. C22×C22⋊Dic181 | C2 | semidirect |
| 3. C22×#15668426 | C2 | semidirect |
| 4. #26041134 | C2 | direct (N × H) |
| 5. C22×C22⋊C4×C181 | C2 | semidirect |
| 9. C24×D181 | C4 | semidirect |
| 12. C23×Dic181 | C22 | semidirect |
| 14. C2×C22⋊Dic181 | C22 | semidirect |
| 16. C2×#15668426 | C22 | semidirect |
| 18. C23×C4×C181 | C22 | semidirect |
| 20. C2×C22⋊C4×C181 | C22 | semidirect |
| 32. C23×D181 | C2×C4 | semidirect |
| 37. C22×Dic181 | C23 | semidirect |
| 48. C22×C4×C181 | C23 | semidirect |
| 62. C22×D181 | C22⋊C4 | semidirect |
| 72. C23×C181 | C22⋊C4 | semidirect |
| 90. C22×C181 | C2×C22⋊C4 | semidirect |
| 103. C2×D181 | C2×C22⋊C4 | semidirect |
| 107. C2×C181 | #379 | semidirect |
| 113. C181 | C2×#379 | semidirect |
| 118. C22×C22⋊C4 | D181 | semidirect |
| 128. C23×C4 | C2×D181 | semidirect |
| 134. C2×C22⋊C4 | C2×D181 | semidirect |
| 160. C22×C4 | C22×D181 | semidirect |
| 183. C23 | #15668426 | semidirect |
| 211. C22 | C2×#15668426 | semidirect |
| 222. C2 | #26041134 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D181 | 2 |
| C22×C22⋊Dic181 | 2 |
| C22×#15668426 | 2 |
| #26041134 | 2 |
| C22×C22⋊C4×C181 | 2 |
| C2×#379 | 181 |