Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
730 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 154 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 | #386 |
| commutator | C22×C4 | C22×C4×C47 |
| Frattini, cosocle | C2×C42 | C23×C47 |
| prime radical | C47×#2541 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C47×#2972 | C2 | semidirect |
| 3. C47×#1800 | C2 | semidirect |
| 4. C47×#1545 | C2 | semidirect |
| 5. C47×#1303 | C2 | semidirect |
| 43. C4⋊C8×C47 | D4 | semidirect |
| 125. #9397 | C47 | direct (N × H) |
| 148. #2972 | C2×C47 | semidirect |
| 150. #1800 | C2×C47 | semidirect |
| 151. #1545 | C2×C47 | semidirect |
| 152. #1303 | C2×C47 | semidirect |
| 174. C47 | #9397 | direct (N × H) |
| 198. C4⋊C8 | D4×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#2972 | 2 |
| C47×#2541 | 2 |
| C47×#1800 | 2 |
| C47×#1545 | 2 |
| C47×#1303 | 2 |
| #9397 | 47 |