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. C13×Dic3⋊C4 | C2 | semidirect |
| 6. Dic3⋊Dic13 | C2 | semidirect |
| 7. #10597612 | C2 | semidirect |
| 18. Dic3×D13 | C4 | semidirect |
| 32. Dic39 | C2×C4 | semidirect |
| 35. Dic3×C13 | C2×C4 | semidirect |
| 50. C3×D13 | C4⋊C4 | semidirect |
| 67. Dic3⋊C4 | D13 | direct (N × H) |
| 68. C3×C13 | C2×C4⋊C4 | semidirect |
| 73. D13 | Dic3⋊C4 | direct (N × H) |
| 91. C13 | C2×Dic3⋊C4 | semidirect |
| 101. Dic3 | C4×D13 | semidirect |
| 126. C3 | C4⋊C4×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D13 | 2 |
| C2×Dic3×D13 | 2 |
| #10597664 | 2 |
| C13×Dic3⋊C4 | 2 |
| Dic3⋊Dic13 | 2 |
| #10597612 | 2 |
| C4⋊C4×D13 | 3 |
| C2×Dic3⋊C4 | 13 |