Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
626 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 175 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. #20241233 | C2 | semidirect |
| 4. #20241232 | C2 | semidirect |
| 5. C47×#1281 | C2 | semidirect |
| 66. C2×C8×C47 | M16 | semidirect |
| 80. C2×C47⋊C8 | M16 | semidirect |
| 132. #1281 | D47 | semidirect |
| 153. C47 | #7919 | semidirect |
| 205. C2×C8 | #10625324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252016 | 2 |
| C2×#97×D47 | 2 |
| #20241233 | 2 |
| #20241232 | 2 |
| C47×#1281 | 2 |
| #7919 | 47 |