Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
772 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 772 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 |
|---|---|---|
| 2. #20252438 | C2 | semidirect |
| 3. #20243318 | C2 | semidirect |
| 4. #20243308 | C2 | semidirect |
| 5. #20241929 | C2 | semidirect |
| 6. #20241264 | C2 | semidirect |
| 7. C47×#1305 | C2 | semidirect |
| 12. #15689276 | C4 | semidirect |
| 14. #15689259 | C4 | semidirect |
| 271. #1305 | D47 | semidirect |
| 307. C47 | #9520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252618 | 2 |
| #20252438 | 2 |
| #20243318 | 2 |
| #20243308 | 2 |
| #20241929 | 2 |
| #20241264 | 2 |
| C47×#1305 | 2 |
| #9520 | 47 |