Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
4086 conjugacy classes of subgroups; only the 811 normal subgroups are shown.
This group has 4086 conjugacy classes of subgroups — too many to draw. Only its 811 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 | #36644 |
| 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×#15689671 | C2 | semidirect |
| 2. #20251786 | C2 | semidirect |
| 3. #20251744 | C2 | semidirect |
| 4. #20251730 | C2 | semidirect |
| 5. #127×Dic47 | C2 | semidirect |
| 6. C43×D47 | C2 | semidirect |
| 7. C47×#2867 | C2 | semidirect |
| 39. C42×D47 | D4 | semidirect |
| 64. C42×C47 | #41 | semidirect |
| 87. C4×D47 | #127 | semidirect |
| 97. C4×C47 | #532 | semidirect |
| 103. #2867 | D47 | semidirect |
| 127. C47 | #36644 | semidirect |
| 174. C42 | #10625352 | semidirect |
| 204. C4 | #15689671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689671 | 2 |
| #20251786 | 2 |
| #20251744 | 2 |
| #20251730 | 2 |
| #127×Dic47 | 2 |
| C43×D47 | 2 |
| C47×#2867 | 2 |
| #36644 | 47 |