Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
344 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 118 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×#102 |
| commutator | C2×C8 | C22×C4×C47 |
| Frattini, cosocle | C4×C8 | C23×C47 |
| prime radical | C47×#3169 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C2×C42×C47 ◁ C2×C4×C8×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#2163 | C2 | semidirect |
| 3. C47×#1564 | C2 | semidirect |
| 4. C47×#1333 | C2 | semidirect |
| 98. #11652 | C47 | direct (N × H) |
| 115. #2163 | C2×C47 | semidirect |
| 116. #1564 | C2×C47 | semidirect |
| 117. #1333 | C2×C47 | semidirect |
| 138. C47 | #11652 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#3169 | 2 |
| C47×#2163 | 2 |
| C47×#1564 | 2 |
| C47×#1333 | 2 |
| #11652 | 47 |