Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
460 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C47 | #99 |
| commutator | C2×C4 | C22×C8×C47 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C47 |
| socle | C22×C47 | C2×#99 |
| prime radical | C22×D4×C47 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C47 ◁ C22×C4×C47 ◁ C2×C4×Q8×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#1461 | C2 | semidirect |
| 3. C47×#1324 | C2 | semidirect |
| 21. #124×C47 | C8 | semidirect |
| 114. #11476 | C47 | direct (N × H) |
| 136. #1461 | C2×C47 | semidirect |
| 137. #1324 | C2×C47 | semidirect |
| 157. C47 | #11476 | direct (N × H) |
| 162. #124 | C8×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#124×C47 | 2 |
| C47×#1461 | 2 |
| C47×#1324 | 2 |
| C47×#1318 | 2 |
| #11476 | 47 |