Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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×#15690554 | C2 | semidirect |
| 2. C2×#15690544 | C2 | semidirect |
| 3. C2×#15690540 | C2 | semidirect |
| 4. #20259874 | C2 | semidirect |
| 5. #20259822 | C2 | semidirect |
| 6. #20259811 | C2 | semidirect |
| 7. #102×C193 | C2 | semidirect |
| 26. Dic386 | D4 | semidirect |
| 39. D4×C193 | D4 | semidirect |
| 64. C193 | #449 | semidirect |
| 71. #102 | D193 | semidirect |
| 98. D4 | D772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690554 | 2 |
| C2×#15690544 | 2 |
| C2×#15690540 | 2 |
| #20259874 | 2 |
| #20259822 | 2 |
| #20259811 | 2 |
| #102×C193 | 2 |
| #449 | 193 |