Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
648 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 106 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 | C22×C4 | C22×C4×C47 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C47 |
| socle | C22×C47 | C2×#99 |
| prime radical | C47×#2388 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C47 ◁ C22×C4×C47 ◁ C2×C4×D4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#99×C47 | C2 | semidirect |
| 3. C47×#1460 | C2 | semidirect |
| 4. C47×#1351 | C2 | semidirect |
| 5. C47×#1343 | C2 | semidirect |
| 6. C22×#41×C47 | C4 | semidirect |
| 11. C47×#395 | C4 | semidirect |
| 13. C47×#394 | C4 | semidirect |
| 19. C4×C22⋊C4×C47 | C4 | semidirect |
| 170. #11725 | C47 | direct (N × H) |
| 204. C4×#99 | C2×C47 | semidirect |
| 205. #1460 | C2×C47 | semidirect |
| 206. #1351 | C2×C47 | semidirect |
| 207. #1343 | C2×C47 | semidirect |
| 216. C22×#41 | C4×C47 | semidirect |
| 221. #395 | C4×C47 | semidirect |
| 223. #394 | C4×C47 | semidirect |
| 229. C4×C22⋊C4 | C4×C47 | semidirect |
| 233. C47 | #11725 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#2388 | 2 |
| C4×#99×C47 | 2 |
| C47×#1460 | 2 |
| C47×#1351 | 2 |
| C47×#1343 | 2 |
| #11725 | 47 |