Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×C4×D724 | C2 | semidirect |
| 3. #26041181 | C2 | semidirect |
| 4. #26041157 | C2 | semidirect |
| 5. #26041145 | C2 | semidirect |
| 6. #376×C181 | C2 | semidirect |
| 10. #19153813 | C4 | semidirect |
| 24. C2×D724 | C2×C4 | semidirect |
| 25. C2×D724 | C2×C4 | semidirect |
| 37. C42×C181 | C2×C4 | semidirect |
| 38. C42×C181 | D4 | semidirect |
| 78. C181 | #2328 | semidirect |
| 85. #376 | D181 | semidirect |
| 116. C42 | C4×D181 | semidirect |
| 117. C42 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153813 | 2 |
| C2×C4×D724 | 2 |
| #26041181 | 2 |
| #26041157 | 2 |
| #26041145 | 2 |
| #376×C181 | 2 |
| #2328 | 181 |