Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
328 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D3×D13 |
| commutator, cosocle | C2×C3×C13 | C24 |
| Frattini | C2 | C22×D3×D13 |
| Fitting | C2×C3×C4×C13 | C22 |
| socle | C22×C3×C13 | C23 |
| hypocenter | C3×C13 | C2×#41 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×D39 | C2 | semidirect |
| 2. C2×C4×D3×C13 | C2 | semidirect |
| 3. C2×C3×C4×D13 | C2 | semidirect |
| 4. C2×#64605 | C2 | semidirect |
| 5. C2×#64604 | C2 | semidirect |
| 6. C2×#64603 | C2 | semidirect |
| 7. C2×#64602 | C2 | semidirect |
| 8. #10597737 | C2 | direct (N × H) |
| 15. C4×D39 | C22 | semidirect |
| 17. C4×D3×C13 | C22 | semidirect |
| 19. C3×C4×D13 | C22 | semidirect |
| 20. #64605 | C22 | semidirect |
| 21. #64604 | C22 | semidirect |
| 22. #64603 | C22 | semidirect |
| 23. #64602 | C22 | semidirect |
| 30. C2×C4×D13 | D3 | semidirect |
| 55. C4×D13 | C2×D3 | semidirect |
| 58. C2×C3×C13 | #41 | semidirect |
| 80. C2×C4×D3 | D13 | semidirect |
| 82. C3×C13 | C2×#41 | semidirect |
| 85. C2×C13 | #235 | semidirect |
| 101. C4×D3 | C2×D13 | semidirect |
| 111. C13 | C2×#235 | semidirect |
| 138. C2×C3 | #6127 | semidirect |
| 153. C3 | C2×#6127 | semidirect |
| 157. C2 | #10597737 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D39 | 2 |
| C2×C4×D3×C13 | 2 |
| C2×C3×C4×D13 | 2 |
| C2×#64605 | 2 |
| C2×#64604 | 2 |
| C2×#64603 | 2 |
| C2×#64602 | 2 |
| #10597737 | 2 |
| C2×#6127 | 3 |
| C2×#235 | 13 |