Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1252 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 230 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 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C47 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C47×#3549 | C2 | semidirect |
| 2. C47×#3151 | C2 | semidirect |
| 3. C47×#1655 | C2 | semidirect |
| 4. C47×#1525 | C2 | semidirect |
| 6. C47×H(3,𝔽4) | C22 | semidirect |
| 11. C2×#127×C47 | C22 | semidirect |
| 12. C47×#496 | C22 | semidirect |
| 15. C4×M16×C47 | C22 | semidirect |
| 16. C47×#329 | C22 | semidirect |
| 82. #19073 | C47 | direct (N × H) |
| 93. #3549 | C2×C47 | semidirect |
| 94. #3151 | C2×C47 | semidirect |
| 95. #1655 | C2×C47 | semidirect |
| 96. #1525 | C2×C47 | semidirect |
| 102. H(3,𝔽4) | C22×C47 | semidirect |
| 107. C2×#127 | C22×C47 | semidirect |
| 108. #496 | C22×C47 | semidirect |
| 111. C4×M16 | C22×C47 | semidirect |
| 112. #329 | C22×C47 | semidirect |
| 113. C47 | #19073 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#3549 | 2 |
| C47×#3151 | 2 |
| C47×#1655 | 2 |
| C47×#1525 | 2 |
| #19073 | 47 |