Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
412 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 96 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. C4×C22⋊#10624382 | C2 | semidirect |
| 3. #26042157 | C2 | semidirect |
| 7. #19153874 | C4 | direct (N × H) |
| 13. C2×#15668428 | C4 | semidirect |
| 14. C2×C22⋊Dic181 | C4 | semidirect |
| 16. C2×C4×Dic181 | C4 | semidirect |
| 17. C23×C4×C181 | C4 | semidirect |
| 20. C22⋊#10624382 | C2×C4 | semidirect |
| 57. C2×Dic181 | C42 | semidirect |
| 65. C23×C181 | C42 | semidirect |
| 92. C4×C181 | #99 | semidirect |
| 103. C181 | C4×#99 | semidirect |
| 111. C23×C4 | #10624382 | semidirect |
| 156. C23 | C4×#10624382 | semidirect |
| 199. C4 | #19153874 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153874 | 2 |
| C4×C22⋊#10624382 | 2 |
| #26042157 | 2 |
| C2×C4×C22⋊D181 | 2 |
| C4×#99 | 181 |