Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#19153805 | C2 | semidirect |
| 3. #41×Dic181 | C2 | semidirect |
| 4. #26041503 | C2 | semidirect |
| 5. #26041496 | C2 | semidirect |
| 6. #26041302 | C2 | semidirect |
| 7. #26041288 | C2 | semidirect |
| 8. #26041285 | C2 | semidirect |
| 9. C2×#137×C181 | C2 | semidirect |
| 18. Q8×Dic181 | C22 | semidirect |
| 20. D4×Dic181 | C22 | semidirect |
| 26. #19153745 | C22 | semidirect |
| 27. #19153740 | C22 | semidirect |
| 32. C2×Q16×C181 | C22 | semidirect |
| 33. C2×SD16×C181 | C22 | semidirect |
| 125. C181 | #3040 | semidirect |
| 127. C2×#137 | D181 | semidirect |
| 141. C2×Q16 | C2×D181 | semidirect |
| 143. C2×SD16 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153841 | 2 |
| C2×#19153805 | 2 |
| #41×Dic181 | 2 |
| #26041503 | 2 |
| #26041496 | 2 |
| #26041302 | 2 |
| #26041288 | 2 |
| #26041285 | 2 |
| C2×#137×C181 | 2 |
| #3040 | 181 |