Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
558 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 558 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 |
|---|---|---|
| 2. #20252107 | C2 | semidirect |
| 3. #20244212 | C2 | semidirect |
| 4. #20242055 | C2 | semidirect |
| 5. #20241949 | C2 | semidirect |
| 6. #20241247 | C2 | semidirect |
| 7. C47×#1275 | C2 | semidirect |
| 11. #15689500 | C4 | semidirect |
| 12. #15689470 | C4 | semidirect |
| 102. C2×C8×C47 | D8 | semidirect |
| 195. #1275 | D47 | semidirect |
| 222. C47 | #9293 | semidirect |
| 304. C2×C8 | D376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254308 | 2 |
| #20252107 | 2 |
| #20244212 | 2 |
| #20242055 | 2 |
| #20241949 | 2 |
| #20241247 | 2 |
| C47×#1275 | 2 |
| #9293 | 47 |