Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
298 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 148 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. C2×#15690565 | C2 | semidirect |
| 2. D193⋊M16 | C2 | direct (N × H) |
| 3. C2×#15690564 | C2 | semidirect |
| 4. C2×#15690563 | C2 | semidirect |
| 6. #15690565 | C22 | semidirect |
| 7. #15690564 | C22 | semidirect |
| 8. #15690563 | C22 | semidirect |
| 9. C2×#13095400 | C22 | semidirect |
| 19. #13095400 | C23 | semidirect |
| 43. C2×D193 | M16 | semidirect |
| 52. C2×C193 | C2×M16 | semidirect |
| 55. D193 | C2×M16 | semidirect |
| 56. C193 | C22×M16 | semidirect |
| 111. C2 | D193⋊M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690565 | 2 |
| D193⋊M16 | 2 |
| C2×#15690564 | 2 |
| C2×#15690563 | 2 |
| C22×C4×D193 | 2 |
| C22×M16 | 193 |