Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
258 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 258 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. C2×#15690534 | C2 | semidirect |
| 3. C2×C22⋊Dic193 | C2 | semidirect |
| 4. C2×#15690532 | C2 | semidirect |
| 5. C2×#15690532 | C2 | semidirect |
| 6. C2×C4×Dic193 | C2 | semidirect |
| 7. C2×C22⋊C4×C193 | C2 | semidirect |
| 11. C2×C22⋊D193 | C4 | semidirect |
| 40. C2×Dic193 | D4 | semidirect |
| 54. C2×C4×C193 | D4 | semidirect |
| 80. Dic193 | C22⋊C4 | semidirect |
| 90. C193 | #390 | semidirect |
| 97. C2×C22⋊C4 | D193 | semidirect |
| 145. C2×C4 | C22⋊D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D193 | 2 |
| C2×#15690534 | 2 |
| C2×C22⋊Dic193 | 2 |
| C2×#15690532 | 2 |
| C2×C4×Dic193 | 2 |
| C2×C22⋊C4×C193 | 2 |
| #390 | 193 |