Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1330 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 158 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 | #379 |
| commutator | C22×C4 | C22×C4×C47 |
| Frattini, cosocle | C23×C4 | C23×C47 |
| prime radical | C47×#3484 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#1783 | C2 | semidirect |
| 3. C47×#1504 | C2 | semidirect |
| 4. C47×#1438 | C2 | semidirect |
| 5. C2×H(5,𝔽2)×C47 | C4 | semidirect |
| 9. C47×#535 | C4 | semidirect |
| 13. C47×#518 | C4 | semidirect |
| 16. C47×#407 | C22 | semidirect |
| 17. C2×#95×C47 | C22 | semidirect |
| 68. C2×Q8×C47 | C22⋊C4 | semidirect |
| 86. C2×D4×C47 | C22⋊C4 | semidirect |
| 102. C4⋊C4×C47 | C22⋊C4 | semidirect |
| 162. #8453 | C47 | direct (N × H) |
| 192. #1783 | C2×C47 | semidirect |
| 193. #1504 | C2×C47 | semidirect |
| 194. #1438 | C2×C47 | semidirect |
| 203. C2×H(5,𝔽2) | C4×C47 | semidirect |
| 207. #535 | C4×C47 | semidirect |
| 211. #518 | C4×C47 | semidirect |
| 214. #407 | C22×C47 | semidirect |
| 215. C2×#95 | C22×C47 | semidirect |
| 218. C47 | #8453 | direct (N × H) |
| 267. C2×Q8 | C22⋊C4×C47 | semidirect |
| 285. C2×D4 | C22⋊C4×C47 | semidirect |
| 301. C4⋊C4 | C22⋊C4×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#3484 | 2 |
| C47×#1783 | 2 |
| C47×#1504 | 2 |
| C47×#1438 | 2 |
| #8453 | 47 |