Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
112 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 49 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, prime radical, cosocle | C22×C3×C13 | C23 |
| Fitting | C3×C13×C4⋊C4 | C2 |
| hypercenter | C4⋊C4 | D39 |
| hypocenter | C3×C13 | #125 |
| LCS | G ▷ C22×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 57. C3×C13 | #125 | semidirect |
| 76. C13 | #889 | semidirect |
| 103. C3 | #88143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C13×C4⋊C4 | 2 |
| C4⋊Dic39 | 2 |
| #10597664 | 2 |
| C4×Dic39 | 2 |
| #88143 | 3 |
| #889 | 13 |