Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
184 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 4. #10597664 | C2 | semidirect |
| 5. C3×#6101 | C2 | semidirect |
| 6. #10597612 | C2 | semidirect |
| 7. #10597611 | C2 | semidirect |
| 18. D3×Dic13 | C4 | semidirect |
| 25. #6101 | D3 | direct (N × H) |
| 32. Dic39 | C2×C4 | semidirect |
| 34. C3×Dic13 | C2×C4 | semidirect |
| 50. D3×C13 | C4⋊C4 | semidirect |
| 60. Dic13 | C4×D3 | semidirect |
| 68. C3×C13 | C2×C4⋊C4 | semidirect |
| 91. C13 | D3×C4⋊C4 | semidirect |
| 115. D3 | #6101 | direct (N × H) |
| 126. C3 | C2×#6101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D3×C13 | 2 |
| C2×D3×Dic13 | 2 |
| #10597664 | 2 |
| C3×#6101 | 2 |
| #10597612 | 2 |
| #10597611 | 2 |
| C2×#6101 | 3 |
| D3×C4⋊C4 | 13 |