Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
124 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 54 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. C3×#6131 | C2 | semidirect |
| 2. C3×#6129 | C2 | semidirect |
| 3. C3×C13×SD16 | C2 | semidirect |
| 4. C3×#6107 | C2 | semidirect |
| 5. C3×#6104 | C2 | semidirect |
| 6. C3×#6095 | C2 | semidirect |
| 7. C3×C8×D13 | C2 | semidirect |
| 8. #88170 | C3 | direct (N × H) |
| 20. #6131 | C2×C3 | semidirect |
| 21. #6129 | C2×C3 | semidirect |
| 22. C13×SD16 | C2×C3 | semidirect |
| 23. #6107 | C2×C3 | semidirect |
| 24. #6104 | C2×C3 | semidirect |
| 25. #6095 | C2×C3 | semidirect |
| 26. C8×D13 | C2×C3 | semidirect |
| 61. C3×SD16 | D13 | semidirect |
| 64. C3×C13 | #135 | semidirect |
| 85. SD16 | C3×D13 | semidirect |
| 88. C13 | C3×#135 | semidirect |
| 118. C3 | #88170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6131 | 2 |
| C3×#6129 | 2 |
| C3×C13×SD16 | 2 |
| C3×#6107 | 2 |
| C3×#6104 | 2 |
| C3×#6095 | 2 |
| C3×C8×D13 | 2 |
| #88170 | 3 |
| C3×#135 | 13 |