Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
340 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 128 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 | C2×C4 | C22×C4×C47 |
| Frattini, cosocle | C22×C4 | C23×C47 |
| prime radical | C22×D4×C47 | C22 |
| LCS | G ▷ C2×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×#107×C47 | C2 | semidirect |
| 3. C2×#103×C47 | C2 | semidirect |
| 5. C2×#97×C47 | C2 | semidirect |
| 6. C47×#391 | C2 | semidirect |
| 12. C2×SD16×C47 | C4 | semidirect |
| 87. C8×C47 | C22⋊C4 | semidirect |
| 106. #1973 | C47 | direct (N × H) |
| 114. C2×#107 | C2×C47 | semidirect |
| 115. C2×#103 | C2×C47 | semidirect |
| 117. C2×#97 | C2×C47 | semidirect |
| 118. #391 | C2×C47 | semidirect |
| 120. C47 | #1973 | direct (N × H) |
| 125. C2×SD16 | C4×C47 | semidirect |
| 200. C8 | C22⋊C4×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×SD16×C47 | 2 |
| C2×#107×C47 | 2 |
| C2×#103×C47 | 2 |
| C2×#102×C47 | 2 |
| C2×#97×C47 | 2 |
| C47×#391 | 2 |
| C47×#390 | 2 |
| #1973 | 47 |