Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1190 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 203 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×#15689859 | C2 | semidirect |
| 3. C2×#15689324 | C2 | semidirect |
| 4. #20242448 | C2 | direct (N × H) |
| 5. C2×#15688853 | C2 | semidirect |
| 6. C2×C47×#331 | C2 | semidirect |
| 11. #15689859 | C22 | semidirect |
| 20. #15689324 | C22 | semidirect |
| 23. #15688853 | C22 | semidirect |
| 26. C47×#331 | C22 | semidirect |
| 164. C2×#331 | D47 | semidirect |
| 167. C2×C47 | #1620 | semidirect |
| 189. #331 | C2×D47 | semidirect |
| 191. C47 | C2×#1620 | semidirect |
| 326. C2 | #20242448 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689859 | 2 |
| C2×#15689499 | 2 |
| C2×#15689324 | 2 |
| #20242448 | 2 |
| C2×#15688853 | 2 |
| C2×C47×#331 | 2 |
| C2×#1620 | 47 |