Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
334 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 112 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 | C2×C4 | C22×C4×C47 |
| Frattini, cosocle | C22×C4 | C23×C47 |
| prime radical | C2×#41×C47 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C22×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C47×#419 | C2 | semidirect |
| 5. C47×#391 | C2 | semidirect |
| 6. C47×#343 | C2 | semidirect |
| 7. C47×#339 | C2 | semidirect |
| 11. #137×C47 | C4 | semidirect |
| 37. C2×Q8×C47 | C2×C4 | semidirect |
| 52. M16×C47 | C2×C4 | semidirect |
| 118. #1882 | C47 | direct (N × H) |
| 128. #419 | C2×C47 | semidirect |
| 129. #391 | C2×C47 | semidirect |
| 130. #343 | C2×C47 | semidirect |
| 131. #339 | C2×C47 | semidirect |
| 132. C47 | #1882 | direct (N × H) |
| 136. #137 | C4×C47 | semidirect |
| 162. C2×Q8 | C2×C4×C47 | semidirect |
| 177. M16 | C2×C4×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#137×C47 | 2 |
| C47×#520 | 2 |
| C2×#104×C47 | 2 |
| C47×#419 | 2 |
| C47×#391 | 2 |
| C47×#343 | 2 |
| C47×#339 | 2 |
| #1882 | 47 |