Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 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. #26041682 | C2 | semidirect |
| 3. #26041617 | C2 | semidirect |
| 4. #26041592 | C2 | semidirect |
| 5. #26041574 | C2 | semidirect |
| 6. #26041566 | C2 | semidirect |
| 7. #26041527 | C2 | semidirect |
| 8. C4×#15668436 | C2 | semidirect |
| 9. #26041357 | C2 | semidirect |
| 10. #26041319 | C2 | semidirect |
| 11. #554×C181 | C2 | semidirect |
| 121. C181 | #3357 | semidirect |
| 124. #554 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041994 | 2 |
| #26041682 | 2 |
| #26041617 | 2 |
| #26041592 | 2 |
| #26041574 | 2 |
| #26041566 | 2 |
| #26041527 | 2 |
| C4×#15668436 | 2 |
| #26041357 | 2 |
| #26041319 | 2 |
| #554×C181 | 2 |
| #3357 | 181 |