Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×D724 | C2 | semidirect |
| 2. #26041607 | C2 | semidirect |
| 3. #26041590 | C2 | semidirect |
| 4. #26041576 | C2 | semidirect |
| 5. #26041491 | C2 | semidirect |
| 6. #26041429 | C2 | semidirect |
| 8. #26041389 | C2 | semidirect |
| 9. #26041377 | C2 | semidirect |
| 10. #26041336 | C2 | semidirect |
| 11. #529×C181 | C2 | semidirect |
| 22. #19153749 | C22 | semidirect |
| 23. #19153747 | C22 | semidirect |
| 24. C4⋊#13089678 | C22 | semidirect |
| 25. #19153740 | C22 | semidirect |
| 26. #19153737 | C22 | semidirect |
| 31. #19153727 | C22 | semidirect |
| 33. #125×C181 | C22 | semidirect |
| 34. #124×C181 | C22 | semidirect |
| 38. C4×Q8×C181 | C22 | semidirect |
| 40. C4×D4×C181 | C22 | semidirect |
| 140. C181 | #3114 | semidirect |
| 142. #529 | D181 | semidirect |
| 158. #125 | C2×D181 | semidirect |
| 159. #124 | C2×D181 | semidirect |
| 163. C4×Q8 | C2×D181 | semidirect |
| 169. C4×D4 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D724 | 2 |
| #26041607 | 2 |
| #26041590 | 2 |
| #26041576 | 2 |
| #26041491 | 2 |
| #26041429 | 2 |
| #26041412 | 2 |
| #26041389 | 2 |
| #26041377 | 2 |
| #26041336 | 2 |
| #529×C181 | 2 |
| #3114 | 181 |