Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
286 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 77 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. C22×C4×D193 | C2 | semidirect |
| 3. C2×#15690532 | C2 | semidirect |
| 4. C2×#15690532 | C2 | semidirect |
| 5. C2×#15690532 | C2 | semidirect |
| 6. #20259806 | C2 | semidirect |
| 7. #95×C193 | C2 | semidirect |
| 12. C2×D772 | C4 | semidirect |
| 35. C22×D193 | C2×C4 | semidirect |
| 44. C2×Dic193 | D4 | semidirect |
| 54. C2×C4×C193 | C2×C4 | semidirect |
| 55. C2×C4×C193 | D4 | semidirect |
| 76. C2×D193 | C22⋊C4 | semidirect |
| 91. C193 | #386 | semidirect |
| 99. #95 | D193 | semidirect |
| 146. C2×C4 | C4×D193 | semidirect |
| 147. C2×C4 | D772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D772 | 2 |
| C22×C4×D193 | 2 |
| C2×#15690532 | 2 |
| #20259806 | 2 |
| #95×C193 | 2 |
| #386 | 193 |