Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. #26041377 | C2 | semidirect |
| 4. C4×#15668436 | C2 | semidirect |
| 5. #26041315 | C2 | semidirect |
| 6. #26041288 | C2 | semidirect |
| 8. #26041235 | C2 | semidirect |
| 9. #519×C181 | C2 | semidirect |
| 11. C2×#15668436 | C4 | semidirect |
| 20. #19153749 | C22 | semidirect |
| 21. #19153747 | C22 | semidirect |
| 22. #19153740 | C22 | semidirect |
| 24. #19153727 | C22 | semidirect |
| 25. C4×#13089678 | C22 | semidirect |
| 28. C4×Q8×C181 | C22 | semidirect |
| 38. #15668436 | C2×C4 | semidirect |
| 39. #15668436 | C2×C4 | semidirect |
| 41. C2×#13089678 | C2×C4 | semidirect |
| 51. C2×Q8×C181 | C2×C4 | semidirect |
| 103. C181 | #2949 | semidirect |
| 106. #519 | D181 | semidirect |
| 122. C4×Q8 | C2×D181 | semidirect |
| 139. C2×Q8 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668436 | 2 |
| #26041753 | 2 |
| #26041377 | 2 |
| C4×#15668436 | 2 |
| #26041315 | 2 |
| #26041288 | 2 |
| #26041283 | 2 |
| #26041235 | 2 |
| #519×C181 | 2 |
| #2949 | 181 |