Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
362 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. #20241358 | C2 | semidirect |
| 57. Q16×C47 | M16 | semidirect |
| 137. C47 | #11664 | semidirect |
| 175. Q16 | #10625329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245191 | 2 |
| #20242144 | 2 |
| #20241358 | 2 |
| C2×C4×Q16×C47 | 2 |
| #11664 | 47 |