Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
228 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C47 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C47 |
| prime radical | C47×H(3,𝔽4) | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C42×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#497 | C2 | semidirect |
| 3. C47×#489 | C2 | semidirect |
| 4. C47×#329 | C2 | semidirect |
| 5. C47×#329 | C2 | semidirect |
| 8. C4⋊Q8×C47 | C22 | semidirect |
| 17. #97×C47 | C22 | semidirect |
| 18. #97×C47 | C22 | semidirect |
| 70. #1659 | C47 | direct (N × H) |
| 76. #497 | C2×C47 | semidirect |
| 77. #489 | C2×C47 | semidirect |
| 78. #329 | C2×C47 | semidirect |
| 79. #329 | C2×C47 | semidirect |
| 80. C47 | #1659 | direct (N × H) |
| 83. C4⋊Q8 | C22×C47 | semidirect |
| 92. #97 | C22×C47 | semidirect |
| 93. #97 | C22×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×H(3,𝔽4) | 2 |
| C47×#497 | 2 |
| C47×#489 | 2 |
| C47×#329 | 2 |
| #1659 | 47 |