Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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 |
|---|---|---|
| 3. C13×#216 | C2 | semidirect |
| 4. C3×#6107 | C2 | semidirect |
| 5. #10597606 | C2 | semidirect |
| 6. #10597605 | C2 | semidirect |
| 24. #6107 | D3 | semidirect |
| 47. D39 | Q16 | semidirect |
| 59. #216 | D13 | semidirect |
| 62. C3×C13 | C2×Q16 | semidirect |
| 84. C13 | D3×Q16 | semidirect |
| 112. C3 | Q16×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D39 | 2 |
| D39⋊Q8 | 2 |
| C13×#216 | 2 |
| C3×#6107 | 2 |
| #10597606 | 2 |
| #10597605 | 2 |
| #10597591 | 2 |
| Q16×D13 | 3 |
| D3×Q16 | 13 |