Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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×#15690538 | C2 | semidirect |
| 2. C22×#13095393 | C2 | semidirect |
| 4. #20259828 | C2 | semidirect |
| 5. #20259811 | C2 | semidirect |
| 6. #20259809 | C2 | semidirect |
| 7. C22⋊C8×C193 | C2 | semidirect |
| 29. #13095393 | D4 | semidirect |
| 39. C22×C193 | M16 | semidirect |
| 55. C193 | #435 | semidirect |
| 62. C22⋊C8 | D193 | semidirect |
| 98. C22 | #15690538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690538 | 2 |
| C22×#13095393 | 2 |
| C4×C22⋊D193 | 2 |
| #20259828 | 2 |
| #20259811 | 2 |
| #20259809 | 2 |
| C22⋊C8×C193 | 2 |
| #435 | 193 |