Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
264 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 84 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. C2×Dic3×D13 | C2 | semidirect |
| 3. #10597671 | C2 | semidirect |
| 4. C13×#217 | C2 | semidirect |
| 5. #10597608 | C2 | semidirect |
| 9. C22×C3×D13 | C4 | semidirect |
| 12. C2×Dic39 | C22 | semidirect |
| 13. C2×Dic3×C13 | C22 | semidirect |
| 21. C22×C3×C13 | C2×C4 | semidirect |
| 26. C2×C3×D13 | C2×C4 | semidirect |
| 32. C22×D13 | Dic3 | semidirect |
| 43. C3×D13 | C22⋊C4 | semidirect |
| 45. C22×C13 | C2×Dic3 | semidirect |
| 50. C2×D13 | C2×Dic3 | semidirect |
| 58. #217 | D13 | direct (N × H) |
| 59. C3×C13 | C2×C22⋊C4 | semidirect |
| 65. D13 | #217 | direct (N × H) |
| 73. C2×Dic3 | C2×D13 | semidirect |
| 79. C13 | C2×#217 | semidirect |
| 86. C22×C3 | C4×D13 | semidirect |
| 109. C22 | Dic3×D13 | semidirect |
| 113. C3 | C22⋊C4×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D13 | 2 |
| C2×Dic3×D13 | 2 |
| #10597671 | 2 |
| C13×#217 | 2 |
| #10597608 | 2 |
| C22⋊C4×D13 | 3 |
| C2×#217 | 13 |