Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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. #26041167 | C2 | semidirect |
| 4. #26041167 | C2 | semidirect |
| 5. #26041166 | C2 | semidirect |
| 6. #26041130 | C2 | semidirect |
| 7. C22⋊C4×Dic181 | C2 | semidirect |
| 8. C4×C22⋊Dic181 | C2 | semidirect |
| 11. #19153797 | C4 | semidirect |
| 34. C22×Dic181 | C2×C4 | semidirect |
| 41. #15668428 | C2×C4 | semidirect |
| 45. C22⋊Dic181 | C2×C4 | semidirect |
| 126. C181 | #2374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153797 | 2 |
| #26041182 | 2 |
| #26041167 | 2 |
| #26041166 | 2 |
| #26041130 | 2 |
| C22⋊C4×Dic181 | 2 |
| C4×C22⋊Dic181 | 2 |
| #386×C181 | 2 |
| #2374 | 181 |