Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
188 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 64 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. C22×C3×Dic13 | C2 | semidirect |
| 3. C2×#64601 | C2 | semidirect |
| 4. C13×#217 | C2 | semidirect |
| 5. #10597612 | C2 | semidirect |
| 6. #10597610 | C2 | semidirect |
| 7. Dic3×Dic13 | C2 | semidirect |
| 11. #64625 | C4 | semidirect |
| 20. C22×Dic13 | D3 | semidirect |
| 28. C22×C3×C13 | C2×C4 | semidirect |
| 32. C2×D39 | C2×C4 | semidirect |
| 33. Dic39 | C2×C4 | semidirect |
| 35. C3×Dic13 | D4 | semidirect |
| 56. C22×C13 | C4×D3 | semidirect |
| 65. Dic13 | #67 | semidirect |
| 69. #217 | D13 | semidirect |
| 73. C3×C13 | C4×D4 | semidirect |
| 97. C13 | C4×#67 | semidirect |
| 100. C22×C3 | C4×D13 | semidirect |
| 130. C22 | #64601 | semidirect |
| 137. C3 | #88135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64625 | 2 |
| C22×C3×Dic13 | 2 |
| C2×#64601 | 2 |
| C13×#217 | 2 |
| #10597612 | 2 |
| #10597610 | 2 |
| Dic3×Dic13 | 2 |
| #88135 | 3 |
| C4×#67 | 13 |