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 |
|---|---|---|
| 1. D3×Q8×C13 | C2 | semidirect |
| 3. C3×C13×SD16 | C2 | semidirect |
| 4. C13×#216 | C2 | semidirect |
| 5. C13×#214 | C2 | semidirect |
| 6. C13×Dic12 | C2 | semidirect |
| 7. C13×ΓL(1,𝔽25) | C2 | semidirect |
| 25. C13×SD16 | D3 | semidirect |
| 45. #915 | C13 | direct (N × H) |
| 56. D3×Q8 | C2×C13 | semidirect |
| 58. C3×SD16 | C2×C13 | semidirect |
| 59. #216 | C2×C13 | semidirect |
| 60. #214 | C2×C13 | semidirect |
| 61. Dic12 | C2×C13 | semidirect |
| 62. ΓL(1,𝔽25) | C2×C13 | semidirect |
| 63. C3×C13 | #137 | semidirect |
| 84. SD16 | D3×C13 | semidirect |
| 86. C13 | #915 | direct (N × H) |
| 115. C3 | C13×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Q8×C13 | 2 |
| C13×#237 | 2 |
| C3×C13×SD16 | 2 |
| C13×#216 | 2 |
| C13×#214 | 2 |
| C13×Dic12 | 2 |
| C13×ΓL(1,𝔽25) | 2 |
| C13×#137 | 3 |
| #915 | 13 |