Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
264 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 95 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×C4×C13 | C2 | semidirect |
| 3. C22×Dic39 | C2 | semidirect |
| 4. #10597666 | C2 | direct (N × H) |
| 9. C22×D39 | C4 | semidirect |
| 12. C2×C3×C4×C13 | C22 | semidirect |
| 14. C2×Dic39 | C22 | semidirect |
| 16. C22×C4×C13 | D3 | semidirect |
| 26. C2×D39 | C2×C4 | semidirect |
| 35. C2×C4×C13 | C2×D3 | semidirect |
| 39. C2×C3×C13 | C22⋊C4 | semidirect |
| 55. C22×C3×C4 | D13 | semidirect |
| 58. C3×C13 | C2×C22⋊C4 | semidirect |
| 60. C2×C13 | (C2×D3)⋊C4 | semidirect |
| 71. C2×C3×C4 | C2×D13 | semidirect |
| 76. C22×C4 | D39 | semidirect |
| 78. C13 | C2×(C2×D3)⋊C4 | semidirect |
| 97. C2×C4 | C2×D39 | semidirect |
| 98. C2×C3 | #6103 | semidirect |
| 113. C3 | C2×#6103 | semidirect |
| 115. C2 | #10597666 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D39 | 2 |
| C22×C3×C4×C13 | 2 |
| C22×Dic39 | 2 |
| #10597666 | 2 |
| C2×#6103 | 3 |
| C2×(C2×D3)⋊C4 | 13 |