Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
388 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 98 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×#99 |
| commutator | C22×C4 | C22×C4×C47 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C47 |
| prime radical | C24×C47 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C22×C4×C47 ◁ C2×#117×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C47×#1346 | C2 | semidirect |
| 115. #11807 | C47 | direct (N × H) |
| 138. #1346 | C2×C47 | semidirect |
| 160. C47 | #11807 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#2621 | 2 |
| C47×#1822 | 2 |
| C47×#1464 | 2 |
| C47×#1346 | 2 |
| #11807 | 47 |