Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #26041757 | C2 | semidirect |
| 4. #26041382 | C2 | semidirect |
| 5. #26041364 | C2 | semidirect |
| 6. #26041315 | C2 | semidirect |
| 8. #26041237 | C2 | semidirect |
| 9. #419×C181 | C2 | semidirect |
| 11. C2×#15668436 | C4 | semidirect |
| 16. Q8×Dic181 | C22 | semidirect |
| 23. #19153749 | C22 | semidirect |
| 24. #19153747 | C22 | semidirect |
| 26. #19153726 | C22 | semidirect |
| 27. C8×Dic181 | C22 | semidirect |
| 31. #103×C181 | C22 | semidirect |
| 38. #15668436 | C2×C4 | semidirect |
| 39. #15668436 | C2×C4 | semidirect |
| 40. C2×#13089678 | C2×C4 | semidirect |
| 54. C2×Q8×C181 | C2×C4 | semidirect |
| 103. C181 | #2949 | semidirect |
| 111. #419 | D181 | semidirect |
| 132. #103 | 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 |
| #26041757 | 2 |
| #26041753 | 2 |
| #26041382 | 2 |
| #26041364 | 2 |
| #26041315 | 2 |
| #26041285 | 2 |
| #26041237 | 2 |
| #419×C181 | 2 |
| #2949 | 181 |