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 |
| 2. C2×#15689320 | C2 | semidirect |
| 3. #20242445 | C2 | direct (N × H) |
| 4. C2×#15688867 | C2 | semidirect |
| 5. C2×#15688855 | C2 | semidirect |
| 10. #15689859 | C22 | semidirect |
| 16. #15689320 | C22 | semidirect |
| 19. #15688867 | C22 | semidirect |
| 20. #15688855 | C22 | semidirect |
| 168. C2×C47 | #1620 | semidirect |
| 191. C47 | C2×#1620 | semidirect |
| 326. C2 | #20242445 | 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×#15689320 | 2 |
| #20242445 | 2 |
| C2×#15688867 | 2 |
| C2×#15688855 | 2 |
| C2×C47×#493 | 2 |
| C2×#1620 | 47 |