Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
782 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 491 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. C2×#15688951 | C2 | direct (N × H) |
| 7. #15688951 | C22 | direct (N × H) |
| 9. C22×C16×C47 | C4 | semidirect |
| 21. C2×C16×C47 | C2×C4 | semidirect |
| 37. C16×C47 | C22×C4 | semidirect |
| 52. C22×C47 | #367 | semidirect |
| 63. C2×C47 | C2×#367 | semidirect |
| 68. C22×C16 | Dic47 | semidirect |
| 73. C47 | C22×#367 | semidirect |
| 82. C2×C16 | C2×Dic47 | semidirect |
| 100. C16 | C22×Dic47 | semidirect |
| 114. C22 | #15688951 | direct (N × H) |
| 122. C2 | C2×#15688951 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13093958 | 2 |
| C2×#15688951 | 2 |
| C23×C16×C47 | 2 |
| C22×#367 | 47 |