Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 1. #20254306 | C2 | semidirect |
| 2. #20252852 | C2 | semidirect |
| 3. #20242056 | C2 | semidirect |
| 4. #20241882 | C2 | semidirect |
| 5. #20241779 | C2 | semidirect |
| 6. #20241291 | C2 | semidirect |
| 7. C47×#2541 | C2 | semidirect |
| 38. #13094024 | D4 | semidirect |
| 39. #13094021 | D4 | semidirect |
| 47. C4⋊(C47⋊C8) | D4 | semidirect |
| 48. C4⋊(C47⋊C8) | D4 | semidirect |
| 102. C2×D4×C47 | D8 | semidirect |
| 235. #2541 | D47 | semidirect |
| 271. C47 | #10238 | semidirect |
| 352. C2×D4 | #10625334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254306 | 2 |
| #20252852 | 2 |
| #20242056 | 2 |
| #20241882 | 2 |
| #20241779 | 2 |
| #20241291 | 2 |
| C47×#2541 | 2 |
| #10238 | 47 |