Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C22×#15668439 | C2 | semidirect |
| 2. C22×#15668437 | C2 | semidirect |
| 3. C22×#15668436 | C2 | semidirect |
| 5. C2×#19153804 | C2 | semidirect |
| 6. #26041661 | C2 | direct (N × H) |
| 7. C2×C4×#13089678 | C2 | semidirect |
| 8. C2×#124×C181 | C2 | semidirect |
| 12. C2×#15668439 | C22 | semidirect |
| 14. C2×#15668437 | C22 | semidirect |
| 16. C2×#15668436 | C22 | semidirect |
| 22. #19153804 | C22 | semidirect |
| 24. C4×#13089678 | C22 | semidirect |
| 28. #124×C181 | C22 | semidirect |
| 112. C2×C181 | #495 | semidirect |
| 116. C181 | C2×#495 | semidirect |
| 123. C2×#124 | D181 | semidirect |
| 143. #124 | C2×D181 | semidirect |
| 230. C2 | #26041661 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668439 | 2 |
| C22×#15668437 | 2 |
| C22×#15668436 | 2 |
| C22×#15668434 | 2 |
| C2×#19153804 | 2 |
| #26041661 | 2 |
| C2×C4×#13089678 | 2 |
| C2×#124×C181 | 2 |
| C2×#495 | 181 |