Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
136 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 2. C8×D39 | C2 | semidirect |
| 3. C13×ΓL(1,𝔽25) | C2 | semidirect |
| 4. C3×#6094 | C2 | semidirect |
| 5. #10597593 | C2 | semidirect |
| 6. #10597592 | C2 | semidirect |
| 7. #10597591 | C2 | semidirect |
| 16. C3×C8×C13 | C22 | semidirect |
| 17. C3⋊#1055 | C22 | semidirect |
| 18. C3×#1055 | C22 | semidirect |
| 19. C13×C3⋊C8 | C22 | semidirect |
| 24. #6094 | D3 | semidirect |
| 43. C8×C13 | C2×D3 | semidirect |
| 45. #1055 | C2×D3 | semidirect |
| 48. D39 | M16 | semidirect |
| 63. ΓL(1,𝔽25) | D13 | semidirect |
| 66. C3×C13 | C2×M16 | semidirect |
| 80. C3×C8 | C2×D13 | semidirect |
| 82. C3⋊C8 | C2×D13 | semidirect |
| 90. C13 | D3×M16 | semidirect |
| 109. C8 | D3×D13 | semidirect |
| 122. C3 | M16×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D3×D13 | 2 |
| C8×D39 | 2 |
| C13×ΓL(1,𝔽25) | 2 |
| C3×#6094 | 2 |
| #10597593 | 2 |
| #10597592 | 2 |
| #10597591 | 2 |
| M16×D13 | 3 |
| D3×M16 | 13 |