Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
156 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 1. C2×C4×D3×C13 | C2 | semidirect |
| 3. #10597664 | C2 | semidirect |
| 4. C3×#6103 | C2 | semidirect |
| 5. #10597611 | C2 | semidirect |
| 6. (C2×D3)⋊Dic13 | C2 | semidirect |
| 7. #10597608 | C2 | semidirect |
| 22. #6103 | D3 | semidirect |
| 65. C2×C4×D3 | D13 | semidirect |
| 71. C3×C13 | #123 | semidirect |
| 94. C13 | #883 | semidirect |
| 133. C3 | #88183 | 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×#64602 | 2 |
| #10597664 | 2 |
| C3×#6103 | 2 |
| #10597611 | 2 |
| (C2×D3)⋊Dic13 | 2 |
| #10597608 | 2 |
| #88183 | 3 |
| #883 | 13 |