Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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. #26041620 | C2 | direct (N × H) |
| 3. C2×#19153749 | C2 | semidirect |
| 4. C2×#19153747 | C2 | semidirect |
| 5. C2×#19153739 | C2 | semidirect |
| 6. C2×#19153739 | C2 | semidirect |
| 17. #19153749 | C22 | semidirect |
| 18. #19153747 | C22 | semidirect |
| 19. #19153739 | C22 | semidirect |
| 20. #19153739 | C22 | semidirect |
| 102. C2×C181 | #485 | semidirect |
| 106. C181 | C2×#485 | semidirect |
| 209. C2 | #26041620 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153795 | 2 |
| #26041620 | 2 |
| C2×#19153749 | 2 |
| C2×#19153747 | 2 |
| C2×#19153739 | 2 |
| C2×C22⋊#13089678 | 2 |
| C2×#117×C181 | 2 |
| C2×#485 | 181 |