Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
264 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 264 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 |
|---|---|---|
| 2. C22×C3×#261 | C2 | semidirect |
| 3. C3×C22⋊#261 | C2 | direct (N × H) |
| 4. C2×C22⋊#261 | C3 | direct (N × H) |
| 5. C23×C3×C13 | C4 | semidirect |
| 7. C22×C3×D13 | C4 | semidirect |
| 8. C22×C3×D13 | C4 | semidirect |
| 12. C2×C3×#261 | C22 | semidirect |
| 14. C22×#261 | C2×C3 | semidirect |
| 15. C22⋊#261 | C2×C3 | direct (N × H) |
| 18. C22×C3×C13 | C2×C4 | semidirect |
| 23. C2×C3×D13 | C2×C4 | semidirect |
| 27. C23×C13 | C3×C4 | semidirect |
| 29. C22×D13 | C3×C4 | semidirect |
| 30. C22×D13 | C3×C4 | semidirect |
| 34. C2×#261 | C22×C3 | semidirect |
| 37. C2×C3×C13 | C22⋊C4 | semidirect |
| 40. C3×D13 | C22⋊C4 | semidirect |
| 44. C22×C13 | C2×C3×C4 | semidirect |
| 49. C2×D13 | C2×C3×C4 | semidirect |
| 56. C3×C13 | C2×C22⋊C4 | semidirect |
| 59. C2×C13 | C3×C22⋊C4 | semidirect |
| 62. D13 | C3×C22⋊C4 | semidirect |
| 69. C23×C3 | #261 | semidirect |
| 75. C13 | C2×C3×C22⋊C4 | semidirect |
| 85. C22×C3 | C2×#261 | semidirect |
| 92. C23 | C3×#261 | semidirect |
| 99. C2×C3 | C22⋊#261 | direct (N × H) |
| 110. C22 | C2×C3×#261 | semidirect |
| 112. C3 | C2×C22⋊#261 | direct (N × H) |
| 117. C2 | C3×C22⋊#261 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D13 | 2 |
| C22×C3×#261 | 2 |
| C3×C22⋊#261 | 2 |
| C2×C22⋊#261 | 3 |
| C2×C3×C22⋊C4 | 13 |