Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 3. #26041631 | C2 | semidirect |
| 4. #26041623 | C2 | semidirect |
| 5. #26041538 | C2 | semidirect |
| 6. #26041490 | C2 | semidirect |
| 7. #26041436 | C2 | semidirect |
| 8. C4×#15668439 | C2 | semidirect |
| 10. #26041286 | C2 | semidirect |
| 11. #475×C181 | C2 | semidirect |
| 121. C181 | #3328 | semidirect |
| 127. #475 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042003 | 2 |
| Q8×D724 | 2 |
| #26041631 | 2 |
| #26041623 | 2 |
| #26041538 | 2 |
| #26041490 | 2 |
| #26041436 | 2 |
| C4×#15668439 | 2 |
| #26041356 | 2 |
| #26041286 | 2 |
| #475×C181 | 2 |
| #3328 | 181 |