Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
282 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C43 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C43 |
| prime radical | C22×D4×C43 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C22×C4×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C43×#544 | C2 | semidirect |
| 4. C43×#343 | C2 | semidirect |
| 5. C43×#339 | C2 | semidirect |
| 22. C2×D4×C43 | Q8 | semidirect |
| 75. #2027 | C43 | direct (N × H) |
| 82. #544 | C2×C43 | semidirect |
| 85. #343 | C2×C43 | semidirect |
| 86. #339 | C2×C43 | semidirect |
| 87. C43 | #2027 | direct (N × H) |
| 104. C2×D4 | Q8×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#544 | 2 |
| C43×#418 | 2 |
| C43×#390 | 2 |
| C43×#343 | 2 |
| C43×#339 | 2 |
| #2027 | 43 |