Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 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 |
|---|---|---|
| 3. #26041658 | C2 | semidirect |
| 5. #26041489 | C2 | semidirect |
| 6. #26041486 | C2 | semidirect |
| 8. #26041410 | C2 | semidirect |
| 9. #26041384 | C2 | semidirect |
| 11. #557×C181 | C2 | semidirect |
| 119. C181 | #3398 | semidirect |
| 121. #557 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042002 | 2 |
| #26041671 | 2 |
| #26041658 | 2 |
| #26041501 | 2 |
| #26041489 | 2 |
| #26041486 | 2 |
| #26041481 | 2 |
| #26041410 | 2 |
| #26041384 | 2 |
| C4×#15668436 | 2 |
| #557×C181 | 2 |
| #3398 | 181 |