Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2070 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D47 |
| commutator, socle, cosocle | C23×C47 | C25 |
| Fitting | C47×#2840 | C2 |
| hypercenter | #2840 | D47 |
| hypocenter | C47 | #36675 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20251579 | C2 | semidirect |
| 2. #20251472 | C2 | semidirect |
| 3. #20251385 | C2 | semidirect |
| 4. #20246670 | C2 | semidirect |
| 5. #20246605 | C2 | semidirect |
| 6. #20245887 | C2 | semidirect |
| 7. C47×#2840 | C2 | semidirect |
| 8. C22×#10625354 | C22 | semidirect |
| 11. C2×Q8×Dic47 | C22 | semidirect |
| 13. #15689065 | C22 | semidirect |
| 14. #15689050 | C22 | semidirect |
| 16. #15689042 | C22 | semidirect |
| 17. #15689041 | C22 | semidirect |
| 19. #15689034 | C22 | semidirect |
| 24. #15688970 | C22 | semidirect |
| 25. #15688968 | C22 | semidirect |
| 57. C24×C47 | #41 | semidirect |
| 126. #2840 | D47 | semidirect |
| 159. C47 | #36675 | semidirect |
| 189. C24 | #10625354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251579 | 2 |
| #20251472 | 2 |
| #20251385 | 2 |
| #20246670 | 2 |
| #20246605 | 2 |
| #20245887 | 2 |
| C47×#2840 | 2 |
| #36675 | 47 |