Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26041762 | C2 | semidirect |
| 3. #26041604 | C2 | semidirect |
| 4. #26041604 | C2 | semidirect |
| 5. #26041598 | C2 | semidirect |
| 6. #26041593 | C2 | semidirect |
| 7. #26041321 | C2 | semidirect |
| 8. #26041317 | C2 | semidirect |
| 9. #26041285 | C2 | semidirect |
| 10. C2×#19153738 | C2 | semidirect |
| 11. #408×C181 | C2 | semidirect |
| 23. #19153775 | C22 | semidirect |
| 25. C2×C4⋊Dic181 | C22 | semidirect |
| 26. #19153750 | C22 | semidirect |
| 27. #19153750 | C22 | semidirect |
| 28. #19153750 | C22 | semidirect |
| 29. #19153748 | C22 | semidirect |
| 30. #19153748 | C22 | semidirect |
| 31. #19153748 | C22 | semidirect |
| 39. C22⋊C8×C181 | C22 | semidirect |
| 40. C22⋊C8×C181 | C22 | semidirect |
| 134. C181 | #3096 | semidirect |
| 146. #408 | D181 | semidirect |
| 174. C22⋊C8 | C2×D181 | semidirect |
| 175. C22⋊C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041843 | 2 |
| #26041762 | 2 |
| #26041604 | 2 |
| #26041598 | 2 |
| #26041593 | 2 |
| #26041321 | 2 |
| #26041317 | 2 |
| #26041285 | 2 |
| C2×#19153738 | 2 |
| #408×C181 | 2 |
| #3096 | 181 |