Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
342 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041675 | C2 | semidirect |
| 3. #26041617 | C2 | semidirect |
| 4. #26041609 | C2 | semidirect |
| 5. #26041571 | C2 | semidirect |
| 6. #26041564 | C2 | semidirect |
| 7. #26041535 | C2 | semidirect |
| 8. C4×#15668439 | C2 | semidirect |
| 10. #26041319 | C2 | semidirect |
| 116. C181 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041999 | 2 |
| #26041675 | 2 |
| #26041617 | 2 |
| #26041609 | 2 |
| #26041571 | 2 |
| #26041564 | 2 |
| #26041535 | 2 |
| C4×#15668439 | 2 |
| #26041357 | 2 |
| #26041319 | 2 |
| #554×C181 | 2 |
| #3356 | 181 |