Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
326 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C47 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C47 |
| prime radical | C22×D4×C47 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C47 ◁ C2×C42×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊Q8×C47 | C2 | semidirect |
| 4. C47×#340 | C2 | semidirect |
| 5. C47×#336 | C2 | semidirect |
| 24. C2×D4×C47 | Q8 | semidirect |
| 88. #2023 | C47 | direct (N × H) |
| 97. C2×C4⋊Q8 | C2×C47 | semidirect |
| 100. #340 | C2×C47 | semidirect |
| 101. #336 | C2×C47 | semidirect |
| 102. C47 | #2023 | direct (N × H) |
| 121. C2×D4 | Q8×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Q8×C47 | 2 |
| C2×#102×C47 | 2 |
| C47×#390 | 2 |
| C47×#340 | 2 |
| C47×#336 | 2 |
| #2023 | 47 |