Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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. C4×Dic3×C13 | C2 | semidirect |
| 3. C3×#6101 | C2 | semidirect |
| 4. #10597612 | C2 | semidirect |
| 5. #10597611 | C2 | semidirect |
| 22. #6101 | D3 | semidirect |
| 61. C4×Dic3 | D13 | semidirect |
| 62. C3×C13 | #126 | semidirect |
| 82. C13 | #898 | semidirect |
| 114. C3 | #88130 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10597666 | 2 |
| C4×Dic3×C13 | 2 |
| C3×#6101 | 2 |
| #10597612 | 2 |
| #10597611 | 2 |
| #10597610 | 2 |
| #88130 | 3 |
| #898 | 13 |