Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
152 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 48 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. C2×#64605 | C2 | semidirect |
| 3. #10597666 | C2 | semidirect |
| 4. C4×Dic3×C13 | C2 | semidirect |
| 5. C3×#6103 | C2 | semidirect |
| 6. #10597610 | C2 | semidirect |
| 7. #10597608 | C2 | semidirect |
| 24. #6103 | D3 | semidirect |
| 70. C4×Dic3 | D13 | semidirect |
| 71. C3×C13 | #124 | semidirect |
| 94. C13 | #885 | semidirect |
| 133. C3 | #88129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64605 | 2 |
| C2×#64603 | 2 |
| #10597666 | 2 |
| C4×Dic3×C13 | 2 |
| C3×#6103 | 2 |
| #10597610 | 2 |
| #10597608 | 2 |
| #88129 | 3 |
| #885 | 13 |