Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
436 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#19153815 | C2 | semidirect |
| 3. #26041637 | C2 | direct (N × H) |
| 4. C2×#19153741 | C2 | semidirect |
| 5. C2×#19153739 | C2 | semidirect |
| 7. C2×#19153726 | C2 | semidirect |
| 13. #19153815 | C22 | semidirect |
| 21. #19153741 | C22 | semidirect |
| 22. #19153739 | C22 | semidirect |
| 24. #19153726 | C22 | semidirect |
| 104. C2×C181 | #489 | semidirect |
| 108. C181 | C2×#489 | semidirect |
| 213. C2 | #26041637 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153815 | 2 |
| C2×#19153803 | 2 |
| #26041637 | 2 |
| C2×#19153741 | 2 |
| C2×#19153739 | 2 |
| C2×#19153737 | 2 |
| C2×#19153726 | 2 |
| C2×#102×C181 | 2 |
| C2×#489 | 181 |