Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
426 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 135 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. C22×D772 | C2 | semidirect |
| 2. C22×D772 | C2 | semidirect |
| 3. C22×C4×D193 | C2 | semidirect |
| 4. #20259874 | C2 | direct (N × H) |
| 5. C2×#15690532 | C2 | semidirect |
| 6. C2×C4⋊C4×C193 | C2 | semidirect |
| 11. C2×D772 | C22 | semidirect |
| 12. C2×D772 | C22 | semidirect |
| 15. C2×C4×D193 | C22 | semidirect |
| 16. #15690532 | C22 | semidirect |
| 19. C4⋊C4×C193 | C22 | semidirect |
| 25. C22×D193 | D4 | semidirect |
| 35. C2×C4×C193 | D4 | semidirect |
| 49. C2×D193 | C2×D4 | semidirect |
| 51. C4×C193 | C2×D4 | semidirect |
| 53. C2×C193 | #121 | semidirect |
| 59. C193 | C2×#121 | semidirect |
| 65. C2×C4⋊C4 | D193 | semidirect |
| 78. C4⋊C4 | C2×D193 | semidirect |
| 95. C2×C4 | D772 | semidirect |
| 112. C4 | C2×D772 | semidirect |
| 115. C2 | #20259874 | direct (N × H) |
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 |
| #20259874 | 2 |
| C2×#15690532 | 2 |
| C2×C4⋊C4×C193 | 2 |
| C2×#121 | 193 |