Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
110 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 37 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. #20259890 | C2 | semidirect |
| 3. #20259821 | C2 | semidirect |
| 4. #20259820 | C2 | semidirect |
| 5. #20259819 | C2 | semidirect |
| 6. #20259809 | C2 | semidirect |
| 7. #102×C193 | C2 | semidirect |
| 52. C193 | #490 | semidirect |
| 59. #102 | D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259895 | 2 |
| #20259890 | 2 |
| #20259821 | 2 |
| #20259820 | 2 |
| #20259819 | 2 |
| #20259809 | 2 |
| #102×C193 | 2 |
| #490 | 193 |