Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
158 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 50 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×#15690563 | C2 | semidirect |
| 2. #20259978 | C2 | semidirect |
| 3. #20259962 | C2 | semidirect |
| 4. #20259961 | C2 | semidirect |
| 12. #15690556 | C4 | semidirect |
| 14. #15690555 | C4 | semidirect |
| 16. #15690554 | C4 | semidirect |
| 22. #41×C193 | C4 | semidirect |
| 68. C193 | #416 | semidirect |
| 80. #41 | #11715871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690563 | 2 |
| #20259978 | 2 |
| #20259962 | 2 |
| #20259961 | 2 |
| #41×D193 | 2 |
| #416 | 193 |