Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#15689539 | C2 | semidirect |
| 3. #20245123 | C2 | semidirect |
| 4. C2×#15688931 | C2 | semidirect |
| 5. #20243439 | C2 | semidirect |
| 6. #20241501 | C2 | semidirect |
| 7. C47×#1382 | C2 | semidirect |
| 16. #15689399 | C4 | semidirect |
| 17. #15689394 | C4 | semidirect |
| 181. #1382 | D47 | semidirect |
| 209. C47 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689539 | 2 |
| #20253109 | 2 |
| #20245123 | 2 |
| C2×#15688931 | 2 |
| #20243439 | 2 |
| #20241501 | 2 |
| C47×#1382 | 2 |
| #13071 | 47 |