Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19153848 | C2 | semidirect |
| 2. C2×#19153843 | C2 | semidirect |
| 3. #26041830 | C2 | semidirect |
| 4. #124×D181 | C2 | semidirect |
| 5. #26041671 | C2 | semidirect |
| 6. #26041669 | C2 | semidirect |
| 7. #26041668 | C2 | semidirect |
| 8. #26041664 | C2 | semidirect |
| 9. #26041660 | C2 | semidirect |
| 10. #26041231 | C2 | semidirect |
| 11. #497×C181 | C2 | semidirect |
| 17. C2×#15668439 | C22 | semidirect |
| 18. C2×#15668438 | C22 | semidirect |
| 20. C2×#15668436 | C22 | semidirect |
| 24. #19153813 | C22 | semidirect |
| 26. #19153805 | C22 | semidirect |
| 34. #19153727 | C22 | semidirect |
| 35. C8×Dic181 | C22 | semidirect |
| 36. C2×Q16×C181 | C22 | semidirect |
| 38. C4⋊Q8×C181 | C22 | semidirect |
| 40. #97×C181 | C22 | semidirect |
| 63. #15668432 | D4 | semidirect |
| 134. C181 | #3153 | semidirect |
| 141. #497 | D181 | semidirect |
| 153. C2×Q16 | C2×D181 | semidirect |
| 161. C4⋊Q8 | C2×D181 | semidirect |
| 174. #97 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153848 | 2 |
| C2×#19153843 | 2 |
| #26041830 | 2 |
| #124×D181 | 2 |
| #26041671 | 2 |
| #26041669 | 2 |
| #26041668 | 2 |
| #26041664 | 2 |
| #26041660 | 2 |
| #26041231 | 2 |
| #497×C181 | 2 |
| #3153 | 181 |