Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
140 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 16. #64605 | C4 | direct (N × H) |
| 25. C3×C4×C13 | Q8 | semidirect |
| 47. C4×C13 | Dic6 | semidirect |
| 59. C3×C13 | C4×Q8 | semidirect |
| 79. C13 | C4×Dic6 | semidirect |
| 83. C3×C4 | Dic26 | semidirect |
| 106. C4 | #64605 | direct (N × H) |
| 107. C3 | C4×Dic26 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64605 | 2 |
| C4×Dic39 | 2 |
| C4×Dic3×C13 | 2 |
| C3×C4×Dic13 | 2 |
| Dic3⋊Dic13 | 2 |
| #10597612 | 2 |
| #10597611 | 2 |
| C4×Dic26 | 3 |
| C4×Dic6 | 13 |