Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
148 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 51 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×Dic78 | C2 | semidirect |
| 3. C3×C13×C4⋊C4 | C2 | semidirect |
| 6. #10597664 | C2 | semidirect |
| 7. #10597664 | C2 | semidirect |
| 20. C13×C4⋊C4 | D3 | semidirect |
| 28. C2×D39 | Q8 | semidirect |
| 61. C3×C4⋊C4 | D13 | semidirect |
| 66. C3×C13 | C22⋊Q8 | semidirect |
| 85. C4⋊C4 | D39 | semidirect |
| 88. C13 | #896 | semidirect |
| 122. C3 | #88150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D39 | 2 |
| C2×Dic78 | 2 |
| C3×C13×C4⋊C4 | 2 |
| #10597666 | 2 |
| #10597664 | 2 |
| #88150 | 3 |
| #896 | 13 |