Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2590 conjugacy classes of subgroups; only the 1054 normal subgroups are shown.
This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 1054 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C47 | D8 |
| commutator, Frattini, cosocle | C8 | C25×C47 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C47 ◁ C23×C4×C47 ◁ C23×C8×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D8×C47 | C2 | semidirect |
| 2. C22×D16×C47 | C2 | direct (N × H) |
| 3. C23×C16×C47 | C2 | semidirect |
| 6. C22×D8×C47 | C22 | semidirect |
| 8. C2×D16×C47 | C22 | direct (N × H) |
| 9. C22×C16×C47 | C22 | semidirect |
| 15. C2×D8×C47 | C23 | semidirect |
| 18. D16×C47 | C23 | direct (N × H) |
| 19. C2×C16×C47 | C23 | semidirect |
| 28. D8×C47 | C24 | semidirect |
| 31. C16×C47 | C24 | semidirect |
| 34. C23×C47 | D16 | direct (N × H) |
| 42. C23×D16 | C47 | direct (N × H) |
| 45. C22×C47 | C2×D16 | direct (N × H) |
| 49. C23×D8 | C2×C47 | semidirect |
| 50. C22×D16 | C2×C47 | direct (N × H) |
| 51. C23×C16 | C2×C47 | semidirect |
| 53. C2×C47 | C22×D16 | direct (N × H) |
| 57. C22×D8 | C22×C47 | semidirect |
| 59. C2×D16 | C22×C47 | direct (N × H) |
| 60. C22×C16 | C22×C47 | semidirect |
| 61. C47 | C23×D16 | direct (N × H) |
| 67. C2×D8 | C23×C47 | semidirect |
| 70. D16 | C23×C47 | direct (N × H) |
| 71. C2×C16 | C23×C47 | semidirect |
| 80. D8 | C24×C47 | semidirect |
| 83. C16 | C24×C47 | semidirect |
| 86. C23 | D16×C47 | direct (N × H) |
| 96. C22 | C2×D16×C47 | direct (N × H) |
| 101. C2 | C22×D16×C47 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D8×C47 | 2 |
| C22×D16×C47 | 2 |
| C23×C16×C47 | 2 |
| C23×D16 | 47 |