Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
756 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 249 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. #26042046 | C2 | semidirect |
| 3. #26041261 | C2 | semidirect |
| 4. C2×#19153732 | C2 | semidirect |
| 5. #568×C181 | C2 | semidirect |
| 13. C2×#15668433 | C22 | semidirect |
| 14. #19153734 | C22 | semidirect |
| 15. #19153732 | C22 | semidirect |
| 18. C2×M16×C181 | C22 | semidirect |
| 76. C181 | #2888 | semidirect |
| 80. #568 | D181 | semidirect |
| 93. C2×M16 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153862 | 2 |
| #26042046 | 2 |
| #26041261 | 2 |
| C2×#19153732 | 2 |
| #568×C181 | 2 |
| #2888 | 181 |