Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. Q8×D724 | C2 | semidirect |
| 3. #26041630 | C2 | semidirect |
| 4. #26041623 | C2 | semidirect |
| 5. #26041574 | C2 | semidirect |
| 6. #26041524 | C2 | semidirect |
| 7. #26041484 | C2 | semidirect |
| 8. #26041416 | C2 | semidirect |
| 9. #26041358 | C2 | semidirect |
| 10. #26041286 | C2 | semidirect |
| 11. C4×SD16×C181 | C2 | semidirect |
| 126. C181 | #3329 | semidirect |
| 136. C4×SD16 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041994 | 2 |
| Q8×D724 | 2 |
| #26041630 | 2 |
| #26041623 | 2 |
| #26041574 | 2 |
| #26041524 | 2 |
| #26041484 | 2 |
| #26041416 | 2 |
| #26041358 | 2 |
| #26041286 | 2 |
| C4×SD16×C181 | 2 |
| #3329 | 181 |