Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
284 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8×C47 | C22⋊C4 |
| commutator | C22 | C2×C42×C47 |
| Frattini, cosocle | C22×C4 | C23×C47 |
| socle | C2×C47 | C4×C22⋊C4 |
| prime radical | C2×#41×C47 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C47 ◁ C22×C8×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C47×#405 | C2 | semidirect |
| 5. C47×#344 | C2 | semidirect |
| 9. C2×M16×C47 | C4 | semidirect |
| 12. C22×C8×C47 | C4 | semidirect |
| 15. #101×C47 | C4 | semidirect |
| 16. #100×C47 | C4 | semidirect |
| 70. #1757 | C47 | direct (N × H) |
| 78. #405 | C2×C47 | semidirect |
| 79. #344 | C2×C47 | semidirect |
| 80. C47 | #1757 | direct (N × H) |
| 84. C2×M16 | C4×C47 | semidirect |
| 87. C22×C8 | C4×C47 | semidirect |
| 90. #101 | C4×C47 | semidirect |
| 91. #100 | C4×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#131×C47 | 2 |
| C47×#413 | 2 |
| C47×#410 | 2 |
| C47×#405 | 2 |
| C47×#344 | 2 |
| #1757 | 47 |