Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
366 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20241353 | C2 | semidirect |
| 5. #20241352 | C2 | semidirect |
| 6. #20241351 | C2 | semidirect |
| 7. C47×#1332 | C2 | semidirect |
| 73. Q16×C47 | M16 | semidirect |
| 97. Dic188 | M16 | semidirect |
| 157. #1332 | D47 | semidirect |
| 181. C47 | #11658 | semidirect |
| 231. Q16 | #10625324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q16×D47 | 2 |
| #20245185 | 2 |
| #20242145 | 2 |
| #20241353 | 2 |
| #20241352 | 2 |
| #20241351 | 2 |
| C47×#1332 | 2 |
| #11658 | 47 |