Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
158 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C43 | #124 |
| commutator, Frattini, cosocle | C22×C4 | C23×C43 |
| socle | C2×C43 | #400 |
| prime radical | C23×C43 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C43 ◁ C22×C4×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 49. #2102 | C43 | direct (N × H) |
| 58. C43 | #2102 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#430 | 2 |
| C43×#423 | 2 |
| C43×#344 | 2 |
| C43×#339 | 2 |
| C43×H(3,ℤ/4) | 2 |
| #2102 | 43 |