Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 3. #26041682 | C2 | semidirect |
| 4. #26041623 | C2 | semidirect |
| 5. #26041618 | C2 | semidirect |
| 6. #26041565 | C2 | semidirect |
| 7. #26041519 | C2 | semidirect |
| 8. C4×#15668439 | C2 | semidirect |
| 10. #26041314 | C2 | semidirect |
| 11. #475×C181 | C2 | semidirect |
| 115. C181 | #3342 | semidirect |
| 123. #475 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042003 | 2 |
| #26042002 | 2 |
| #26041682 | 2 |
| #26041623 | 2 |
| #26041618 | 2 |
| #26041565 | 2 |
| #26041519 | 2 |
| C4×#15668439 | 2 |
| #26041344 | 2 |
| #26041314 | 2 |
| #475×C181 | 2 |
| #3342 | 181 |