Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19153839 | C2 | semidirect |
| 2. C2×#19153837 | C2 | semidirect |
| 3. #26041830 | C2 | semidirect |
| 4. #26041828 | C2 | semidirect |
| 5. #26041672 | C2 | semidirect |
| 6. #26041671 | C2 | semidirect |
| 7. #26041669 | C2 | semidirect |
| 8. #26041668 | C2 | semidirect |
| 9. #26041665 | C2 | semidirect |
| 10. #97×D181 | C2 | semidirect |
| 11. #497×C181 | C2 | semidirect |
| 65. C8×D181 | D4 | semidirect |
| 133. C181 | #3150 | semidirect |
| 141. #497 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153839 | 2 |
| C2×#19153837 | 2 |
| #26041830 | 2 |
| #26041828 | 2 |
| #26041672 | 2 |
| #26041671 | 2 |
| #26041669 | 2 |
| #26041668 | 2 |
| #26041665 | 2 |
| #97×D181 | 2 |
| #497×C181 | 2 |
| #3150 | 181 |