Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
752 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 1. C2×#15689107 | C2 | semidirect |
| 2. C2×#15688920 | C2 | semidirect |
| 3. #20243316 | C2 | semidirect |
| 4. #20241515 | C2 | semidirect |
| 34. #13093943 | D4 | semidirect |
| 281. C47 | #13093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689107 | 2 |
| C2×#15688920 | 2 |
| #20243316 | 2 |
| #20241515 | 2 |
| C47×#2431 | 2 |
| #13093 | 47 |