Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 200 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. #26042290 | C2 | semidirect |
| 3. #26042289 | C2 | semidirect |
| 12. #19153885 | C22 | semidirect |
| 13. #19153884 | C22 | semidirect |
| 15. C2×#15668433 | C4 | semidirect |
| 16. C2×#15668432 | C4 | semidirect |
| 17. M16×D181 | C4 | semidirect |
| 20. C2×M16×C181 | C4 | semidirect |
| 38. #15668433 | C2×C4 | semidirect |
| 39. #15668432 | C2×C4 | semidirect |
| 40. C2×#13089678 | C2×C4 | semidirect |
| 41. C8×D181 | C2×C4 | semidirect |
| 44. M16×C181 | C2×C4 | semidirect |
| 45. C2×C8×C181 | C2×C4 | semidirect |
| 97. C181 | #2911 | semidirect |
| 108. C2×M16 | #10624382 | semidirect |
| 133. M16 | C2×#10624382 | semidirect |
| 137. C2×C8 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153895 | 2 |
| #26042290 | 2 |
| #26042289 | 2 |
| C2×M16×D181 | 2 |
| #2911 | 181 |