Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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 |
|---|---|---|
| 3. #10597670 | C2 | semidirect |
| 4. C13×#216 | C2 | semidirect |
| 5. #10597605 | C2 | semidirect |
| 6. #10597604 | C2 | semidirect |
| 47. C3×D13 | Q16 | semidirect |
| 60. #216 | D13 | direct (N × H) |
| 62. C3×C13 | C2×Q16 | semidirect |
| 65. D13 | #216 | direct (N × H) |
| 84. C13 | C2×#216 | semidirect |
| 112. C3 | Q16×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×D13 | 2 |
| Dic6×D13 | 2 |
| #10597670 | 2 |
| C13×#216 | 2 |
| #10597605 | 2 |
| #10597604 | 2 |
| C3⋊C8×D13 | 2 |
| Q16×D13 | 3 |
| C2×#216 | 13 |