Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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. Q8×D39 | C2 | semidirect |
| 3. C3×C13×SD16 | C2 | semidirect |
| 4. #10597670 | C2 | semidirect |
| 5. #10597668 | C2 | semidirect |
| 6. Dic156 | C2 | semidirect |
| 7. #10597657 | C2 | semidirect |
| 22. C13×SD16 | D3 | semidirect |
| 58. C3×SD16 | D13 | semidirect |
| 63. C3×C13 | #137 | semidirect |
| 84. SD16 | D39 | semidirect |
| 86. C13 | #915 | semidirect |
| 115. C3 | #88169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D39 | 2 |
| #10597792 | 2 |
| C3×C13×SD16 | 2 |
| #10597670 | 2 |
| #10597668 | 2 |
| Dic156 | 2 |
| #10597657 | 2 |
| #88169 | 3 |
| #915 | 13 |