Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
156 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D39 |
| commutator, socle, cosocle | C22×C3×C13 | C23 |
| Fitting, prime radical | C2×C3×D4×C13 | C2 |
| hypercenter | C2×D4 | D39 |
| hypocenter | C3×C13 | #123 |
| LCS | G ▷ C22×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic39 | C2 | semidirect |
| 3. #10597671 | C2 | semidirect |
| 4. #10597671 | C2 | semidirect |
| 5. #10597664 | C2 | semidirect |
| 52. C3×C13 | #123 | semidirect |
| 70. C13 | #935 | semidirect |
| 98. C3 | #88189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C13 | 2 |
| C22×Dic39 | 2 |
| #10597671 | 2 |
| #10597664 | 2 |
| #88189 | 3 |
| #935 | 13 |