Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
108 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 35 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. #20259927 | C2 | semidirect |
| 2. #20259925 | C2 | semidirect |
| 3. C2×#15690540 | C2 | semidirect |
| 4. #20259907 | C2 | semidirect |
| 5. #20259834 | C2 | semidirect |
| 6. #20259815 | C2 | semidirect |
| 7. #100×C193 | C2 | semidirect |
| 53. C193 | #472 | semidirect |
| 61. #100 | D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259927 | 2 |
| #20259925 | 2 |
| C2×#15690540 | 2 |
| #20259907 | 2 |
| #20259834 | 2 |
| #20259815 | 2 |
| #100×C193 | 2 |
| #472 | 193 |