Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×#19153887 | C2 | semidirect |
| 3. #26042286 | C2 | semidirect |
| 5. #26042149 | C2 | semidirect |
| 6. (C2×#10624382)⋊C8 | C2 | semidirect |
| 23. #19153740 | C4 | semidirect |
| 24. #19153738 | C4 | semidirect |
| 25. #19153736 | C4 | semidirect |
| 26. #103×C181 | C4 | semidirect |
| 109. C181 | #1866 | semidirect |
| 134. #103 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153904 | 2 |
| C2×#19153887 | 2 |
| #26042286 | 2 |
| C2×#19153881 | 2 |
| #26042149 | 2 |
| (C2×#10624382)⋊C8 | 2 |
| #26041274 | 2 |
| #1866 | 181 |