Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. C2×#19153838 | C2 | semidirect |
| 2. C2×#19153836 | C2 | semidirect |
| 3. #26041825 | C2 | semidirect |
| 4. #26041672 | C2 | semidirect |
| 5. #26041670 | C2 | semidirect |
| 6. #26041667 | C2 | semidirect |
| 7. #26041665 | C2 | semidirect |
| 8. C2×#19153726 | C2 | semidirect |
| 9. C2×#135×C181 | C2 | semidirect |
| 51. C2×#13089678 | D4 | semidirect |
| 68. C2×C8×C181 | D4 | semidirect |
| 116. C181 | #3150 | semidirect |
| 120. C2×#135 | D181 | semidirect |
| 180. C2×C8 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153838 | 2 |
| C2×#19153836 | 2 |
| #26041825 | 2 |
| #26041672 | 2 |
| #26041670 | 2 |
| #26041667 | 2 |
| #26041665 | 2 |
| C2×#19153726 | 2 |
| C2×#135×C181 | 2 |
| #3150 | 181 |