Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
156 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 46 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. C2×#64601 | C2 | semidirect |
| 3. #10597666 | C2 | semidirect |
| 4. C13×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C3×C4⋊Dic13 | C2 | semidirect |
| 6. #10597612 | C2 | semidirect |
| 7. (C2×D3)⋊Dic13 | C2 | semidirect |
| 23. C4⋊Dic13 | D3 | semidirect |
| 69. (C2×D3)⋊C4 | D13 | semidirect |
| 71. C3×C13 | #123 | semidirect |
| 94. C13 | #894 | semidirect |
| 133. C3 | #88137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64604 | 2 |
| C2×#64601 | 2 |
| #10597666 | 2 |
| C13×(C2×D3)⋊C4 | 2 |
| C3×C4⋊Dic13 | 2 |
| #10597612 | 2 |
| (C2×D3)⋊Dic13 | 2 |
| #88137 | 3 |
| #894 | 13 |