Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
426 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 127 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×C22⋊D193 | C2 | semidirect |
| 3. C22×C22⋊D193 | C2 | semidirect |
| 4. C22×C4×D193 | C2 | semidirect |
| 5. #20259872 | C2 | direct (N × H) |
| 6. C2×#15690534 | C2 | semidirect |
| 7. C2×#15690532 | C2 | semidirect |
| 8. C2×C22⋊C4×C193 | C2 | semidirect |
| 12. C2×D772 | C22 | semidirect |
| 15. C2×C22⋊D193 | C22 | semidirect |
| 16. C2×C22⋊D193 | C22 | semidirect |
| 20. C2×C4×D193 | C22 | semidirect |
| 21. #15690534 | C22 | semidirect |
| 22. #15690532 | C22 | semidirect |
| 26. C22⋊C4×C193 | C22 | semidirect |
| 32. C22×D193 | D4 | semidirect |
| 39. C2×Dic193 | D4 | semidirect |
| 67. C2×D193 | C2×D4 | semidirect |
| 71. Dic193 | C2×D4 | semidirect |
| 73. C2×C193 | #121 | semidirect |
| 79. C193 | C2×#121 | semidirect |
| 88. C2×C22⋊C4 | D193 | semidirect |
| 106. C22⋊C4 | C2×D193 | semidirect |
| 155. C2 | #20259872 | 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×C22⋊D193 | 2 |
| C22×C4×D193 | 2 |
| #20259872 | 2 |
| C2×#15690534 | 2 |
| C2×#15690532 | 2 |
| C2×C22⋊C4×C193 | 2 |
| C2×#121 | 193 |