Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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. #20259987 | C2 | semidirect |
| 2. #20259986 | C2 | semidirect |
| 3. #20259970 | C2 | semidirect |
| 4. #20259964 | C2 | semidirect |
| 5. #20259963 | C2 | semidirect |
| 6. #20259953 | C2 | semidirect |
| 18. #15690545 | C4 | semidirect |
| 19. #15690544 | C4 | semidirect |
| 20. #15690540 | C4 | semidirect |
| 22. SD16×C193 | C4 | semidirect |
| 51. C193 | #444 | semidirect |
| 64. SD16 | #11715871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259987 | 2 |
| #20259986 | 2 |
| #20259970 | 2 |
| #20259964 | 2 |
| #20259963 | 2 |
| #20259953 | 2 |
| #20259920 | 2 |
| #444 | 193 |