Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20245189 | C2 | semidirect |
| 3. #20242142 | C2 | semidirect |
| 4. #20241359 | C2 | semidirect |
| 5. #20241357 | C2 | semidirect |
| 6. #20241355 | C2 | semidirect |
| 7. C47×#1333 | C2 | semidirect |
| 74. D8×C47 | M16 | semidirect |
| 97. Dic188 | M16 | semidirect |
| 158. #1333 | D47 | semidirect |
| 183. C47 | #11666 | semidirect |
| 234. D8 | #10625324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13094043 | 2 |
| #20245189 | 2 |
| #20242142 | 2 |
| #20241359 | 2 |
| #20241357 | 2 |
| #20241355 | 2 |
| C47×#1333 | 2 |
| #11666 | 47 |