Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26041649 | C2 | semidirect |
| 3. #26041641 | C2 | semidirect |
| 4. #26041636 | C2 | semidirect |
| 5. #26041631 | C2 | semidirect |
| 6. #26041287 | C2 | semidirect |
| 9. C2×#19153739 | C2 | semidirect |
| 10. #26041235 | C2 | semidirect |
| 11. #544×C181 | C2 | semidirect |
| 127. C181 | #3137 | semidirect |
| 129. #544 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041855 | 2 |
| #26041649 | 2 |
| #26041641 | 2 |
| #26041636 | 2 |
| #26041631 | 2 |
| #26041287 | 2 |
| #26041278 | 2 |
| #26041273 | 2 |
| C2×#19153739 | 2 |
| #26041235 | 2 |
| #544×C181 | 2 |
| #3137 | 181 |