Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
630 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C47 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C8×C47 |
| Frattini, cosocle | C2×C42 | C23×C47 |
| prime radical | C24×C47 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C47 ◁ C22×C42×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C47×#1272 | C2 | semidirect |
| 18. C22×Q8×C47 | C8 | semidirect |
| 104. #7595 | C47 | direct (N × H) |
| 124. #1272 | C2×C47 | semidirect |
| 141. C47 | #7595 | direct (N × H) |
| 146. C22×Q8 | C8×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C47×#391 | 2 |
| C47×#1817 | 2 |
| C47×#1272 | 2 |
| #7595 | 47 |