Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
300 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 74 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. #26042152 | C2 | semidirect |
| 4. #26042152 | C2 | semidirect |
| 13. #19153775 | C4 | semidirect |
| 14. #19153774 | C4 | semidirect |
| 15. #19153774 | C4 | semidirect |
| 22. #117×C181 | C4 | semidirect |
| 109. C181 | #1825 | semidirect |
| 123. #117 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊(C22⋊C8) | 2 |
| #26042221 | 2 |
| #26042152 | 2 |
| #117×D181 | 2 |
| #1825 | 181 |