Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
558 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20252105 | C2 | semidirect |
| 3. #20244211 | C2 | semidirect |
| 4. #20242057 | C2 | semidirect |
| 5. #20241947 | C2 | semidirect |
| 6. #20241218 | C2 | semidirect |
| 7. C47×#1286 | C2 | semidirect |
| 11. #15689500 | C4 | semidirect |
| 12. #15689470 | C4 | semidirect |
| 115. C2×C47⋊C8 | D8 | semidirect |
| 194. #1286 | D47 | semidirect |
| 222. C47 | #9293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254308 | 2 |
| #20252105 | 2 |
| #20244211 | 2 |
| #20242057 | 2 |
| #20241947 | 2 |
| #20241218 | 2 |
| C47×#1286 | 2 |
| #9293 | 47 |