Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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×C22⋊C4×C23 | C2 | semidirect |
| 3. C2×C22⋊Dic23 | C2 | semidirect |
| 4. C4×C22⋊D23 | C2 | semidirect |
| 5. (C22⋊D23)⋊C4 | C2 | semidirect |
| 6. C22⋊C4×D23 | C2 | semidirect |
| 7. #10625048 | C2 | semidirect |
| 10. C22×C4×C23 | C22 | semidirect |
| 11. C2×C22⋊D23 | C4 | semidirect |
| 15. C22×Dic23 | C22 | semidirect |
| 16. C2×C4×D23 | C22 | semidirect |
| 18. C22⋊C4×C23 | C22 | semidirect |
| 20. C22⋊Dic23 | C22 | semidirect |
| 21. (C2×D23)⋊C4 | C22 | semidirect |
| 22. Dic23⋊C4 | C22 | semidirect |
| 23. C4×Dic23 | C22 | semidirect |
| 25. C23×C23 | C2×C4 | semidirect |
| 30. C22×D23 | C2×C4 | semidirect |
| 34. C22⋊D23 | C2×C4 | semidirect |
| 35. C22⋊D23 | C2×C4 | semidirect |
| 37. C2×Dic23 | C2×C4 | semidirect |
| 68. C2×C22⋊C4 | D23 | semidirect |
| 69. C23 | #518 | semidirect |
| 78. C22×C4 | C2×D23 | semidirect |
| 84. C22⋊C4 | C2×D23 | semidirect |
| 90. C23 | C4×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D23 | 2 |
| C2×C22⋊C4×C23 | 2 |
| C2×C22⋊Dic23 | 2 |
| C4×C22⋊D23 | 2 |
| (C22⋊D23)⋊C4 | 2 |
| C22⋊C4×D23 | 2 |
| #10625048 | 2 |
| #518 | 23 |