Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19153841 | C2 | semidirect |
| 2. C22×D1448 | C2 | semidirect |
| 3. #26041843 | C2 | semidirect |
| 4. #26041665 | C2 | semidirect |
| 5. #26041664 | C2 | semidirect |
| 6. #26041654 | C2 | semidirect |
| 7. #26041234 | C2 | semidirect |
| 8. C2×#135×C181 | C2 | semidirect |
| 11. C2×#15668436 | C22 | semidirect |
| 15. C2×#15668434 | C22 | semidirect |
| 17. #19153812 | C22 | semidirect |
| 18. #19153805 | C22 | semidirect |
| 22. #19153726 | C22 | semidirect |
| 23. C8×Dic181 | C22 | semidirect |
| 26. C2×Q16×C181 | C22 | semidirect |
| 27. C2×SD16×C181 | C22 | semidirect |
| 28. C2×D8×C181 | C22 | semidirect |
| 40. #15668433 | D4 | semidirect |
| 56. C2×C8×C181 | D4 | semidirect |
| 101. C181 | #3155 | semidirect |
| 104. C2×#135 | D181 | semidirect |
| 115. C2×Q16 | C2×D181 | semidirect |
| 117. C2×SD16 | C2×D181 | semidirect |
| 122. C2×D8 | C2×D181 | semidirect |
| 154. C2×C8 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153841 | 2 |
| C22×D1448 | 2 |
| #26041843 | 2 |
| #26041665 | 2 |
| #26041664 | 2 |
| #26041654 | 2 |
| #26041234 | 2 |
| C2×#135×C181 | 2 |
| #3155 | 181 |