Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
528 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19153815 | C2 | semidirect |
| 3. #26041624 | C2 | direct (N × H) |
| 4. C2×#19153738 | C2 | semidirect |
| 5. C2×#19153737 | C2 | semidirect |
| 6. C2×#19153736 | C2 | semidirect |
| 7. C2×C8×Dic181 | C2 | semidirect |
| 8. C2×#102×C181 | C2 | semidirect |
| 15. #19153815 | C22 | semidirect |
| 21. #19153738 | C22 | semidirect |
| 22. #19153737 | C22 | semidirect |
| 23. #19153736 | C22 | semidirect |
| 24. C8×Dic181 | C22 | semidirect |
| 28. #102×C181 | C22 | semidirect |
| 113. C2×C181 | #486 | semidirect |
| 118. C181 | C2×#486 | semidirect |
| 126. C2×#102 | D181 | semidirect |
| 146. #102 | C2×D181 | semidirect |
| 233. C2 | #26041624 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153815 | 2 |
| C2×#19153812 | 2 |
| #26041624 | 2 |
| C2×#19153738 | 2 |
| C2×#19153737 | 2 |
| C2×#19153736 | 2 |
| C2×C8×Dic181 | 2 |
| C2×#102×C181 | 2 |
| C2×#486 | 181 |