Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
184 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 92 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. C3×C4⋊#261 | C2 | direct (N × H) |
| 4. C2×C4⋊#261 | C3 | direct (N × H) |
| 8. C2×C3×C4×C13 | C4 | semidirect |
| 9. C2×C3×Dic13 | C4 | semidirect |
| 10. C3×C4×D13 | C4 | semidirect |
| 14. C4⋊#261 | C2×C3 | direct (N × H) |
| 21. C3×C4×C13 | C2×C4 | semidirect |
| 22. C3×Dic13 | C2×C4 | semidirect |
| 26. C2×C4×C13 | C3×C4 | semidirect |
| 27. C2×Dic13 | C3×C4 | semidirect |
| 28. C4×D13 | C3×C4 | semidirect |
| 31. C2×C3×C13 | C4⋊C4 | semidirect |
| 33. C3×D13 | C4⋊C4 | semidirect |
| 42. C4×C13 | C2×C3×C4 | semidirect |
| 43. Dic13 | C2×C3×C4 | semidirect |
| 47. C3×C13 | C2×C4⋊C4 | semidirect |
| 49. C2×C13 | C3×C4⋊C4 | semidirect |
| 51. D13 | C3×C4⋊C4 | semidirect |
| 60. C2×C3×C4 | #261 | semidirect |
| 64. C13 | C2×C3×C4⋊C4 | semidirect |
| 72. C3×C4 | C2×#261 | semidirect |
| 79. C2×C4 | C3×#261 | semidirect |
| 83. C2×C3 | C4⋊#261 | direct (N × H) |
| 92. C4 | C2×C3×#261 | semidirect |
| 93. C3 | C2×C4⋊#261 | direct (N × H) |
| 97. C2 | C3×C4⋊#261 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#261 | 2 |
| C2×C3×C4×D13 | 2 |
| C3×C4⋊#261 | 2 |
| C2×C4⋊#261 | 3 |
| C2×C3×C4⋊C4 | 13 |