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. C2×C8×D193 | C2 | semidirect |
| 4. C4⋊#13095393 | C2 | semidirect |
| 5. #20259811 | C2 | semidirect |
| 6. #20259811 | C2 | semidirect |
| 7. #97×C193 | C2 | semidirect |
| 36. C8×C193 | D4 | semidirect |
| 43. C2×D193 | M16 | semidirect |
| 55. C193 | #435 | semidirect |
| 63. #97 | D193 | semidirect |
| 92. C8 | D772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690538 | 2 |
| C2×C8×D193 | 2 |
| C4×D772 | 2 |
| C4⋊#13095393 | 2 |
| #20259811 | 2 |
| #97×C193 | 2 |
| #435 | 193 |