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. C13×#239 | C2 | semidirect |
| 2. C13×#237 | C2 | semidirect |
| 3. C3×C13×SD16 | C2 | semidirect |
| 4. C13×#216 | C2 | semidirect |
| 5. C13×#213 | C2 | semidirect |
| 6. C13×#204 | C2 | semidirect |
| 7. D3×C8×C13 | C2 | semidirect |
| 24. C13×SD16 | D3 | semidirect |
| 45. #916 | C13 | direct (N × H) |
| 57. #239 | C2×C13 | semidirect |
| 58. #237 | C2×C13 | semidirect |
| 59. C3×SD16 | C2×C13 | semidirect |
| 60. #216 | C2×C13 | semidirect |
| 61. #213 | C2×C13 | semidirect |
| 62. #204 | C2×C13 | semidirect |
| 63. D3×C8 | C2×C13 | semidirect |
| 64. C3×C13 | #135 | semidirect |
| 85. SD16 | D3×C13 | semidirect |
| 88. C13 | #916 | direct (N × H) |
| 118. C3 | C13×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#239 | 2 |
| C13×#237 | 2 |
| C3×C13×SD16 | 2 |
| C13×#216 | 2 |
| C13×#213 | 2 |
| C13×#204 | 2 |
| D3×C8×C13 | 2 |
| C13×#135 | 3 |
| #916 | 13 |