Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
152 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 72 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 | semidirect |
| 4. C3×C4×#261 | C2 | semidirect |
| 5. #88237 | C3 | direct (N × H) |
| 8. C2×C3×C4×C13 | C4 | semidirect |
| 9. C2×C3×Dic13 | C4 | semidirect |
| 10. C3×C4×D13 | C4 | semidirect |
| 11. C3×C4×D13 | C4 | semidirect |
| 16. C4⋊#261 | C2×C3 | semidirect |
| 17. C4×#261 | C2×C3 | semidirect |
| 29. C2×C4×C13 | C3×C4 | semidirect |
| 30. C2×Dic13 | C3×C4 | semidirect |
| 31. C4×D13 | C3×C4 | semidirect |
| 32. C4×D13 | C3×C4 | semidirect |
| 53. C3×C13 | #117 | semidirect |
| 66. C2×C3×C4 | #261 | semidirect |
| 71. C13 | C3×#117 | semidirect |
| 88. C2×C4 | C3×#261 | semidirect |
| 102. C3 | #88237 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D13 | 2 |
| C3×C22⋊#261 | 2 |
| C3×C4⋊#261 | 2 |
| C3×C4×#261 | 2 |
| #88237 | 3 |
| C3×#117 | 13 |