Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
276 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 57. Q16×C47 | Q16 | semidirect |
| 142. C47 | #12405 | semidirect |
| 176. Q16 | #10625337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256277 | 2 |
| #20245661 | 2 |
| #20242779 | 2 |
| #20241442 | 2 |
| #20241366 | 2 |
| #20241352 | 2 |
| C47×#2225 | 2 |
| #12405 | 47 |