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. #26041631 | C2 | semidirect |
| 4. #26041622 | C2 | semidirect |
| 5. #26041526 | C2 | semidirect |
| 6. #26041485 | C2 | semidirect |
| 7. #26041419 | C2 | semidirect |
| 8. C4×#15668436 | C2 | semidirect |
| 9. #26041356 | C2 | semidirect |
| 10. #26041286 | C2 | semidirect |
| 11. #477×C181 | C2 | semidirect |
| 126. C181 | #3329 | semidirect |
| 132. #477 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041995 | 2 |
| Q8×D724 | 2 |
| #26041631 | 2 |
| #26041622 | 2 |
| #26041526 | 2 |
| #26041485 | 2 |
| #26041419 | 2 |
| C4×#15668436 | 2 |
| #26041356 | 2 |
| #26041286 | 2 |
| #477×C181 | 2 |
| #3329 | 181 |