Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 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 |
|---|---|---|
| 2. C3×Q8×D13 | C2 | semidirect |
| 3. C3×C13×Q16 | C2 | semidirect |
| 4. C3×#6107 | C2 | semidirect |
| 5. C3×#6106 | C2 | semidirect |
| 6. C3×#6095 | C2 | semidirect |
| 7. C3×#6094 | C2 | semidirect |
| 8. #88172 | C3 | direct (N × H) |
| 21. Q8×D13 | C2×C3 | semidirect |
| 22. C13×Q16 | C2×C3 | semidirect |
| 23. #6107 | C2×C3 | semidirect |
| 24. #6106 | C2×C3 | semidirect |
| 25. #6095 | C2×C3 | semidirect |
| 26. #6094 | C2×C3 | semidirect |
| 59. C3×Q16 | D13 | semidirect |
| 63. C3×C13 | #137 | semidirect |
| 82. Q16 | C3×D13 | semidirect |
| 86. C13 | C3×#137 | semidirect |
| 115. C3 | #88172 | 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×Q8×D13 | 2 |
| C3×C13×Q16 | 2 |
| C3×#6107 | 2 |
| C3×#6106 | 2 |
| C3×#6095 | 2 |
| C3×#6094 | 2 |
| #88172 | 3 |
| C3×#137 | 13 |