Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 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 |
|---|---|---|
| 2. C22×#15668439 | C2 | semidirect |
| 3. C22×#15668438 | C2 | semidirect |
| 4. C2×#19153796 | C2 | semidirect |
| 5. #26041444 | C2 | direct (N × H) |
| 6. C2×#19153736 | C2 | semidirect |
| 7. C2×#19153728 | C2 | semidirect |
| 8. C2×#103×C181 | C2 | semidirect |
| 19. C2×#15668439 | C22 | semidirect |
| 21. C2×#15668438 | C22 | semidirect |
| 24. #19153796 | C22 | semidirect |
| 27. #19153736 | C22 | semidirect |
| 28. #19153728 | C22 | semidirect |
| 32. #103×C181 | C22 | semidirect |
| 129. C2×C181 | #452 | semidirect |
| 135. C181 | C2×#452 | semidirect |
| 142. C2×#103 | D181 | semidirect |
| 166. #103 | C2×D181 | semidirect |
| 267. C2 | #26041444 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668450 | 2 |
| C22×#15668439 | 2 |
| C22×#15668438 | 2 |
| C2×#19153796 | 2 |
| #26041444 | 2 |
| C2×#19153736 | 2 |
| C2×#19153728 | 2 |
| C2×#103×C181 | 2 |
| C2×#452 | 181 |