Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
318 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 2. C2×#103×C47 | C2 | semidirect |
| 3. C2×#103×C47 | C2 | semidirect |
| 6. C47×#389 | C2 | semidirect |
| 7. C47×#336 | C2 | semidirect |
| 121. #2042 | C47 | direct (N × H) |
| 131. C2×#103 | C2×C47 | semidirect |
| 132. C2×#103 | C2×C47 | semidirect |
| 135. #389 | C2×C47 | semidirect |
| 136. #336 | C2×C47 | semidirect |
| 137. C47 | #2042 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#124×C47 | 2 |
| C2×#103×C47 | 2 |
| C2×#102×C47 | 2 |
| C47×#389 | 2 |
| C47×#336 | 2 |
| #2042 | 47 |