Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
412 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 412 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×#19153807 | C2 | semidirect |
| 3. #26041632 | C2 | direct (N × H) |
| 4. C2×#19153741 | C2 | semidirect |
| 5. C2×#19153739 | C2 | semidirect |
| 7. C2×C8×Dic181 | C2 | semidirect |
| 12. #19153807 | C22 | semidirect |
| 21. #19153741 | C22 | semidirect |
| 22. #19153739 | C22 | semidirect |
| 24. C8×Dic181 | C22 | semidirect |
| 102. C2×C181 | #488 | semidirect |
| 106. C181 | C2×#488 | semidirect |
| 209. C2 | #26041632 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153807 | 2 |
| C2×#19153803 | 2 |
| #26041632 | 2 |
| C2×#19153741 | 2 |
| C2×#19153739 | 2 |
| C2×#19153737 | 2 |
| C2×C8×Dic181 | 2 |
| C2×#102×C181 | 2 |
| C2×#488 | 181 |