Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
122 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×Dic193 | C2 | semidirect |
| 3. #20259831 | C2 | semidirect |
| 4. #20259823 | C2 | semidirect |
| 6. C8×Dic193 | C2 | semidirect |
| 18. SD16×C193 | C4 | semidirect |
| 28. Q8×C193 | C2×C4 | semidirect |
| 33. C8×C193 | C2×C4 | semidirect |
| 44. Dic193 | SD16 | direct (N × H) |
| 49. C193 | C4×SD16 | semidirect |
| 61. SD16 | Dic193 | direct (N × H) |
| 72. Q8 | C2×Dic193 | semidirect |
| 83. C8 | C2×Dic193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic193 | 2 |
| D4×Dic193 | 2 |
| #20259831 | 2 |
| #20259823 | 2 |
| #20259820 | 2 |
| C8×Dic193 | 2 |
| C2×SD16×C193 | 2 |
| C4×SD16 | 193 |