Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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. #26042243 | C2 | semidirect |
| 4. #26042160 | C2 | semidirect |
| 8. C2×#15668459 | C4 | semidirect |
| 9. C2×#15668458 | C4 | semidirect |
| 12. C2×D181⋊C8 | C4 | semidirect |
| 13. C22×#13089685 | C4 | semidirect |
| 15. #19153877 | C4 | semidirect |
| 16. #19153876 | C4 | semidirect |
| 97. C181 | #1757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153903 | 2 |
| #26042266 | 2 |
| #26042243 | 2 |
| #26042160 | 2 |
| #26041251 | 2 |
| #1757 | 181 |