Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
260 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 64 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×C47 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C47 |
| prime radical | C47×#538 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C22×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#451 | C2 | semidirect |
| 3. C47×#448 | C2 | semidirect |
| 4. C47×#393 | C2 | semidirect |
| 5. C47×#328 | C2 | semidirect |
| 6. C47×#327 | C2 | semidirect |
| 7. C47×#323 | C2 | semidirect |
| 113. #1606 | C47 | direct (N × H) |
| 122. #451 | C2×C47 | semidirect |
| 123. #448 | C2×C47 | semidirect |
| 124. #393 | C2×C47 | semidirect |
| 125. #328 | C2×C47 | semidirect |
| 126. #327 | C2×C47 | semidirect |
| 127. #323 | C2×C47 | semidirect |
| 128. C47 | #1606 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#538 | 2 |
| C47×#451 | 2 |
| C47×#448 | 2 |
| C47×#393 | 2 |
| C47×#328 | 2 |
| C47×#327 | 2 |
| C47×#323 | 2 |
| #1606 | 47 |