Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2022 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 2022 conjugacy classes of subgroups — too many to draw. Only its 587 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. #20251579 | C2 | direct (N × H) |
| 2. C2×#15689065 | C2 | semidirect |
| 4. C2×#15689042 | C2 | semidirect |
| 11. #15689065 | C22 | semidirect |
| 13. #15689042 | C22 | semidirect |
| 114. C2×C47 | #2835 | semidirect |
| 133. C47 | C2×#2835 | semidirect |
| 219. C2 | #20251579 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251579 | 2 |
| C2×#15689065 | 2 |
| C2×#15689048 | 2 |
| C2×#15689042 | 2 |
| C2×#15688995 | 2 |
| C2×C47×#393 | 2 |
| C2×#2835 | 47 |