Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
228 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 76 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 | C42 | C23×C47 |
| prime radical | C2×D4×C47 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C42×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#487 | C2 | semidirect |
| 3. C47×#477 | C2 | semidirect |
| 5. C47×#332 | C2 | semidirect |
| 6. C47×Q8⋊C8 | C2 | semidirect |
| 86. #1637 | C47 | direct (N × H) |
| 92. #487 | C2×C47 | semidirect |
| 93. #477 | C2×C47 | semidirect |
| 95. #332 | C2×C47 | semidirect |
| 96. Q8⋊C8 | C2×C47 | semidirect |
| 98. C47 | #1637 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Q8×C47 | 2 |
| C47×#487 | 2 |
| C47×#477 | 2 |
| C47×#476 | 2 |
| C47×#332 | 2 |
| C47×Q8⋊C8 | 2 |
| C47×D4⋊C8 | 2 |
| #1637 | 47 |