Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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×Q8×D193 | C2 | semidirect |
| 3. #20259897 | C2 | semidirect |
| 4. #20259888 | C2 | semidirect |
| 5. #20259887 | C2 | semidirect |
| 6. #20259884 | C2 | semidirect |
| 7. #20259877 | C2 | semidirect |
| 8. #20259856 | C2 | semidirect |
| 9. C4⋊Q8×C193 | C2 | semidirect |
| 63. C193 | #536 | semidirect |
| 68. C4⋊Q8 | D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690556 | 2 |
| C2×Q8×D193 | 2 |
| #20259897 | 2 |
| #20259888 | 2 |
| #20259887 | 2 |
| #20259884 | 2 |
| #20259877 | 2 |
| #20259856 | 2 |
| C4⋊Q8×C193 | 2 |
| #536 | 193 |