Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 2. C2×#19153774 | C2 | semidirect |
| 3. #26041605 | C2 | direct (N × H) |
| 4. C2×#19153749 | C2 | semidirect |
| 5. C2×#19153738 | C2 | semidirect |
| 6. C2×#19153736 | C2 | semidirect |
| 7. C2×#19153728 | C2 | semidirect |
| 8. C2×#106×C181 | C2 | semidirect |
| 16. #19153774 | C22 | semidirect |
| 21. #19153749 | C22 | semidirect |
| 22. #19153738 | C22 | semidirect |
| 23. #19153736 | C22 | semidirect |
| 24. #19153728 | C22 | semidirect |
| 28. #106×C181 | C22 | semidirect |
| 108. C2×C181 | #482 | semidirect |
| 114. C181 | C2×#482 | semidirect |
| 120. C2×#106 | D181 | semidirect |
| 140. #106 | C2×D181 | semidirect |
| 225. C2 | #26041605 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153791 | 2 |
| C2×#19153774 | 2 |
| #26041605 | 2 |
| C2×#19153749 | 2 |
| C2×#19153738 | 2 |
| C2×#19153736 | 2 |
| C2×#19153728 | 2 |
| C2×#106×C181 | 2 |
| C2×#482 | 181 |