Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
124 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 38 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. #10597792 | C2 | semidirect |
| 2. #10597734 | C2 | semidirect |
| 3. C13×#213 | C2 | semidirect |
| 4. C3×#6105 | C2 | semidirect |
| 5. #10597605 | C2 | semidirect |
| 6. #10597602 | C2 | semidirect |
| 7. #10597591 | C2 | semidirect |
| 24. #6105 | D3 | semidirect |
| 61. #213 | D13 | semidirect |
| 64. C3×C13 | #135 | semidirect |
| 88. C13 | #916 | semidirect |
| 118. C3 | #88166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10597792 | 2 |
| #10597734 | 2 |
| C13×#213 | 2 |
| C3×#6105 | 2 |
| #10597605 | 2 |
| #10597602 | 2 |
| #10597591 | 2 |
| #88166 | 3 |
| #916 | 13 |