Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
152 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 58 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. C4×Dic3×C13 | C2 | semidirect |
| 4. C3×#6101 | C2 | semidirect |
| 5. #10597611 | C2 | semidirect |
| 7. Dic3×Dic13 | C2 | semidirect |
| 16. #64601 | C4 | semidirect |
| 22. #6101 | D3 | semidirect |
| 63. C4×Dic3 | D13 | semidirect |
| 64. C3×C13 | #117 | semidirect |
| 85. C13 | #892 | semidirect |
| 118. C3 | #88126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64601 | 2 |
| #10597666 | 2 |
| C4×Dic3×C13 | 2 |
| C3×#6101 | 2 |
| #10597611 | 2 |
| #10597610 | 2 |
| Dic3×Dic13 | 2 |
| #88126 | 3 |
| #892 | 13 |