Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
304 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C47 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C47 |
| Frattini, cosocle | C22×C4 | C23×C47 |
| socle | C22×C47 | C2×C22⋊C4 |
| prime radical | C47×#525 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C47 ◁ C23×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊C8×C47 | C2 | semidirect |
| 3. C4×C22⋊C4×C47 | C2 | semidirect |
| 4. C47×#328 | C2 | semidirect |
| 5. C47×#327 | C2 | semidirect |
| 6. C2×#41×C47 | C4 | semidirect |
| 10. C22⋊Q8×C47 | C4 | semidirect |
| 12. #121×C47 | C4 | semidirect |
| 17. #117×C47 | C4 | semidirect |
| 105. #1501 | C47 | direct (N × H) |
| 114. C2×C22⋊C8 | C2×C47 | semidirect |
| 115. C4×C22⋊C4 | C2×C47 | semidirect |
| 116. #328 | C2×C47 | semidirect |
| 117. #327 | C2×C47 | semidirect |
| 118. C47 | #1501 | direct (N × H) |
| 119. C2×#41 | C4×C47 | semidirect |
| 123. C22⋊Q8 | C4×C47 | semidirect |
| 125. #121 | C4×C47 | semidirect |
| 130. #117 | C4×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#525 | 2 |
| C2×C22⋊C8×C47 | 2 |
| C4×C22⋊C4×C47 | 2 |
| C47×#328 | 2 |
| C47×#327 | 2 |
| #1501 | 47 |