Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
8094 conjugacy classes of subgroups; only the 1123 normal subgroups are shown.
This group has 8094 conjugacy classes of subgroups — too many to draw. Only its 1123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D47 |
| commutator, socle, cosocle | C23×C47 | C25 |
| Fitting | C47×#2867 | C2 |
| hypercenter | #2867 | D47 |
| hypocenter | C47 | C2×#2867 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #2867 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#127×D47 | C2 | semidirect |
| 2. #20251783 | C2 | semidirect |
| 3. #20251782 | C2 | semidirect |
| 4. C43×D47 | C2 | semidirect |
| 5. C47×#2867 | C2 | semidirect |
| 7. C2×#13094021 | C22 | semidirect |
| 8. C2×#13094020 | C22 | semidirect |
| 11. C42×Dic47 | C22 | semidirect |
| 12. C2×#127×C47 | C22 | semidirect |
| 13. C43×C47 | C22 | semidirect |
| 22. C42×D47 | D4 | semidirect |
| 37. C42×C47 | C2×D4 | semidirect |
| 38. C4×Dic47 | C2×D4 | semidirect |
| 49. C4×D47 | #127 | semidirect |
| 56. C4×C47 | C2×#127 | semidirect |
| 57. Dic47 | C2×#127 | semidirect |
| 61. #2867 | D47 | direct (N × H) |
| 66. D47 | #2867 | direct (N × H) |
| 71. C2×#127 | C2×D47 | semidirect |
| 74. C43 | C2×D47 | semidirect |
| 75. C47 | C2×#2867 | semidirect |
| 100. C42 | D4×D47 | semidirect |
| 118. C4 | #127×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#127×D47 | 2 |
| #20251783 | 2 |
| #20251782 | 2 |
| C43×D47 | 2 |
| C47×#2867 | 2 |
| C2×#2867 | 47 |