Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
408 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 1. C2×#19153875 | C2 | semidirect |
| 2. #26042221 | C2 | semidirect |
| 3. C4×C22⋊#10624382 | C2 | semidirect |
| 12. C22×D724 | C4 | semidirect |
| 19. C2×#15668426 | C4 | semidirect |
| 20. C2×C4⋊C4×C181 | C4 | semidirect |
| 26. C22⋊#10624382 | D4 | semidirect |
| 104. C4×C181 | #99 | semidirect |
| 115. C181 | #1964 | semidirect |
| 129. C2×C4⋊C4 | #10624382 | semidirect |
| 222. C4 | #19153875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153875 | 2 |
| #26042221 | 2 |
| C4×C22⋊#10624382 | 2 |
| C2×#19153791 | 2 |
| #1964 | 181 |