Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
418 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 207 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. C2×C4⋊C4×C23 | C2 | semidirect |
| 4. C2×C4⋊Dic23 | C2 | semidirect |
| 5. C2×Dic23⋊C4 | C2 | semidirect |
| 6. C4⋊C4×D23 | C2 | direct (N × H) |
| 13. C2×C4×D23 | C4 | semidirect |
| 16. C4⋊C4×C23 | C22 | semidirect |
| 17. C4⋊Dic23 | C22 | semidirect |
| 18. Dic23⋊C4 | C22 | semidirect |
| 25. C2×C4×C23 | C2×C4 | semidirect |
| 29. C2×Dic23 | C2×C4 | semidirect |
| 33. C4×D23 | C2×C4 | semidirect |
| 38. C2×D23 | C4⋊C4 | direct (N × H) |
| 43. C4×C23 | C22×C4 | semidirect |
| 45. Dic23 | C22×C4 | semidirect |
| 47. C2×C23 | C2×C4⋊C4 | semidirect |
| 51. D23 | C2×C4⋊C4 | direct (N × H) |
| 57. C2×C4⋊C4 | D23 | direct (N × H) |
| 58. C23 | C22×C4⋊C4 | semidirect |
| 70. C4⋊C4 | C2×D23 | direct (N × H) |
| 83. C2×C4 | C4×D23 | semidirect |
| 97. C4 | C2×C4×D23 | semidirect |
| 99. C2 | C4⋊C4×D23 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D23 | 2 |
| C2×C4⋊C4×C23 | 2 |
| C2×C4⋊Dic23 | 2 |
| C2×Dic23⋊C4 | 2 |
| C4⋊C4×D23 | 2 |
| C22×C4⋊C4 | 23 |