Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
380 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #364×D47 | C2 | semidirect |
| 3. #20241673 | C2 | semidirect |
| 4. #20241365 | C2 | semidirect |
| 5. #20241364 | C2 | semidirect |
| 6. #20241363 | C2 | semidirect |
| 7. C47×#1336 | C2 | semidirect |
| 20. #15688944 | C22 | semidirect |
| 22. #15688844 | C22 | semidirect |
| 25. C47×#364 | C22 | semidirect |
| 26. C47×#322 | C22 | semidirect |
| 28. #13094047 | C8 | semidirect |
| 32. #13094043 | C8 | semidirect |
| 33. Q16×D47 | C8 | semidirect |
| 35. D8×D47 | C8 | semidirect |
| 181. #1336 | D47 | semidirect |
| 203. #364 | C2×D47 | semidirect |
| 205. #322 | C2×D47 | semidirect |
| 207. C47 | #11604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #443×D47 | 2 |
| #364×D47 | 2 |
| #20241673 | 2 |
| #20241365 | 2 |
| #20241364 | 2 |
| #20241363 | 2 |
| C47×#1336 | 2 |
| #11604 | 47 |