Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #26041622 | C2 | semidirect |
| 4. #26041618 | C2 | semidirect |
| 5. #26041614 | C2 | semidirect |
| 6. #26041610 | C2 | semidirect |
| 7. #26041607 | C2 | semidirect |
| 8. #26041320 | C2 | semidirect |
| 9. #26041286 | C2 | semidirect |
| 11. #484×C181 | C2 | semidirect |
| 30. #19153749 | C22 | semidirect |
| 31. #19153748 | C22 | semidirect |
| 32. #19153747 | C22 | semidirect |
| 33. #19153741 | C22 | semidirect |
| 34. #19153740 | C22 | semidirect |
| 35. #19153739 | C22 | semidirect |
| 40. #107×C181 | C22 | semidirect |
| 41. #103×C181 | C22 | semidirect |
| 139. C181 | #3095 | semidirect |
| 146. #484 | D181 | semidirect |
| 173. #107 | C2×D181 | semidirect |
| 179. #103 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊Q8×D181 | 2 |
| C2×#19153774 | 2 |
| #26041622 | 2 |
| #26041618 | 2 |
| #26041614 | 2 |
| #26041610 | 2 |
| #26041607 | 2 |
| #26041320 | 2 |
| #26041286 | 2 |
| #26041241 | 2 |
| #484×C181 | 2 |
| #3095 | 181 |