Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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×#19153804 | C2 | semidirect |
| 2. #26041661 | C2 | semidirect |
| 3. #26041636 | C2 | semidirect |
| 4. #26041501 | C2 | semidirect |
| 5. #26041494 | C2 | semidirect |
| 6. #26041434 | C2 | semidirect |
| 7. #26041429 | C2 | semidirect |
| 8. #26041417 | C2 | semidirect |
| 10. #26041332 | C2 | semidirect |
| 11. #529×C181 | C2 | semidirect |
| 14. C2×#15668439 | C22 | semidirect |
| 15. C2×#15668437 | C22 | semidirect |
| 24. C4⋊#13089678 | C22 | semidirect |
| 25. #19153739 | C22 | semidirect |
| 26. #19153739 | C22 | semidirect |
| 31. C4×#13089678 | C22 | semidirect |
| 33. #125×C181 | C22 | semidirect |
| 34. #124×C181 | C22 | semidirect |
| 38. C4×Q8×C181 | C22 | semidirect |
| 40. C4×D4×C181 | C22 | semidirect |
| 143. C181 | #3211 | semidirect |
| 145. #529 | D181 | semidirect |
| 163. #125 | C2×D181 | semidirect |
| 168. #124 | C2×D181 | semidirect |
| 172. C4×Q8 | C2×D181 | semidirect |
| 174. 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×#19153804 | 2 |
| #26041661 | 2 |
| #26041636 | 2 |
| #26041501 | 2 |
| #26041494 | 2 |
| #26041434 | 2 |
| #26041429 | 2 |
| #26041417 | 2 |
| #26041412 | 2 |
| #26041332 | 2 |
| #529×C181 | 2 |
| #3211 | 181 |