Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
492 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. C2×#15688927 | C2 | semidirect |
| 5. #20241497 | C2 | semidirect |
| 6. #20241483 | C2 | semidirect |
| 7. C47×#2141 | C2 | semidirect |
| 13. #15689395 | C4 | semidirect |
| 51. #13093960 | C2×C4 | semidirect |
| 63. C2×Q16×C47 | C2×C4 | semidirect |
| 178. #2141 | D47 | semidirect |
| 209. C47 | #12997 | semidirect |
| 220. C2×Q16 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689395 | 2 |
| #20251985 | 2 |
| C2×#15688927 | 2 |
| C2×#15688908 | 2 |
| #20241497 | 2 |
| #20241483 | 2 |
| C47×#2141 | 2 |
| #12997 | 47 |