Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 70 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. C22×Dic39 | C2 | semidirect |
| 3. C2×Dic3×D13 | C2 | semidirect |
| 4. C13×#217 | C2 | semidirect |
| 5. #10597611 | C2 | semidirect |
| 6. #10597608 | C2 | semidirect |
| 7. Dic3×Dic13 | C2 | semidirect |
| 16. C3×C22⋊D13 | C4 | semidirect |
| 28. C22×C3×C13 | C2×C4 | semidirect |
| 32. C2×C3×D13 | C2×C4 | semidirect |
| 34. Dic39 | D4 | semidirect |
| 35. C3×Dic13 | C2×C4 | semidirect |
| 42. C22⋊D13 | Dic3 | semidirect |
| 56. C22×C13 | C2×Dic3 | semidirect |
| 60. C2×D13 | C2×Dic3 | semidirect |
| 65. Dic13 | C2×Dic3 | semidirect |
| 70. #217 | D13 | semidirect |
| 73. C3×C13 | C4×D4 | semidirect |
| 97. C13 | D4×Dic3 | semidirect |
| 103. C22×C3 | C4×D13 | semidirect |
| 130. C22 | Dic3×D13 | semidirect |
| 137. C3 | #88135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic39 | 2 |
| C2×C3×C22⋊D13 | 2 |
| C2×Dic3×D13 | 2 |
| C13×#217 | 2 |
| #10597611 | 2 |
| #10597608 | 2 |
| Dic3×Dic13 | 2 |
| #88135 | 3 |
| D4×Dic3 | 13 |