Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D181 | C2 | semidirect |
| 3. C2×#19153792 | C2 | semidirect |
| 4. #26041534 | C2 | semidirect |
| 5. #26041522 | C2 | semidirect |
| 6. #26041517 | C2 | semidirect |
| 7. #26041505 | C2 | semidirect |
| 8. #26041321 | C2 | semidirect |
| 9. #26041288 | C2 | semidirect |
| 10. #26041280 | C2 | semidirect |
| 11. C2×#137×C181 | C2 | semidirect |
| 33. #19153750 | C22 | semidirect |
| 34. #19153748 | C22 | semidirect |
| 35. #19153740 | C22 | semidirect |
| 36. #19153740 | C22 | semidirect |
| 37. #19153740 | C22 | semidirect |
| 38. #19153737 | C22 | semidirect |
| 42. C2×Q16×C181 | C22 | semidirect |
| 43. C2×SD16×C181 | C22 | semidirect |
| 90. M16×C181 | D4 | semidirect |
| 145. C2×D181 | #137 | semidirect |
| 163. C181 | #3056 | semidirect |
| 165. C2×#137 | D181 | semidirect |
| 180. C2×Q16 | C2×D181 | semidirect |
| 181. C2×SD16 | C2×D181 | semidirect |
| 236. M16 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D181 | 2 |
| #26041786 | 2 |
| C2×#19153792 | 2 |
| #26041534 | 2 |
| #26041522 | 2 |
| #26041517 | 2 |
| #26041505 | 2 |
| #26041321 | 2 |
| #26041288 | 2 |
| #26041280 | 2 |
| C2×#137×C181 | 2 |
| #3056 | 181 |