Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 40 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. C3×#6131 | C2 | semidirect |
| 2. #10597738 | C2 | semidirect |
| 3. #10597670 | C2 | semidirect |
| 4. C13×#215 | C2 | semidirect |
| 5. #10597600 | C2 | semidirect |
| 6. #10597595 | C2 | semidirect |
| 7. C3⋊C8×D13 | C2 | semidirect |
| 20. #6131 | D3 | semidirect |
| 60. #215 | D13 | semidirect |
| 64. C3×C13 | #135 | semidirect |
| 88. C13 | #950 | semidirect |
| 118. C3 | #88170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6131 | 2 |
| #10597738 | 2 |
| #10597670 | 2 |
| C13×#215 | 2 |
| #10597600 | 2 |
| #10597595 | 2 |
| C3⋊C8×D13 | 2 |
| #88170 | 3 |
| #950 | 13 |