Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. #20241752 | C2 | semidirect |
| 5. #20241276 | C2 | semidirect |
| 6. #20241231 | C2 | semidirect |
| 7. C2×C47×#328 | C2 | semidirect |
| 10. #15689453 | C4 | semidirect |
| 11. #15689436 | C4 | semidirect |
| 15. #15689279 | C4 | semidirect |
| 16. #15689262 | C4 | semidirect |
| 228. C2×#328 | D47 | semidirect |
| 268. C47 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254169 | 2 |
| #20252442 | 2 |
| #20241890 | 2 |
| #20241752 | 2 |
| #20241276 | 2 |
| #20241231 | 2 |
| C2×C47×#328 | 2 |
| #9263 | 47 |