Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041834 | C2 | semidirect |
| 3. #26041632 | C2 | semidirect |
| 4. #26041631 | C2 | semidirect |
| 5. #26041630 | C2 | semidirect |
| 6. #26041625 | C2 | semidirect |
| 7. #26041272 | C2 | semidirect |
| 8. C4×C8×D181 | C2 | semidirect |
| 9. #486×C181 | C2 | semidirect |
| 111. C181 | #3131 | semidirect |
| 119. #486 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| #26041827 | 2 |
| #26041632 | 2 |
| #26041631 | 2 |
| #26041630 | 2 |
| #26041625 | 2 |
| #26041272 | 2 |
| C4×C8×D181 | 2 |
| #486×C181 | 2 |
| #3131 | 181 |