Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 230 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 |
|---|---|---|
| 19. #19153748 | C4 | semidirect |
| 20. #19153747 | C4 | semidirect |
| 21. #19153747 | C4 | semidirect |
| 22. #106×C181 | C4 | semidirect |
| 107. C181 | #1920 | semidirect |
| 128. #106 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042230 | 2 |
| C4⋊C4×#10624382 | 2 |
| #26042153 | 2 |
| #26042152 | 2 |
| (C2×#10624382)⋊C8 | 2 |
| #106×D181 | 2 |
| #1920 | 181 |