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. #20259898 | C2 | semidirect |
| 4. #20259885 | C2 | semidirect |
| 5. #20259884 | C2 | semidirect |
| 6. #20259881 | C2 | semidirect |
| 7. #20259879 | C2 | semidirect |
| 8. #20259878 | C2 | semidirect |
| 9. #20259875 | C2 | semidirect |
| 10. #20259857 | C2 | semidirect |
| 11. C22⋊Q8×C193 | C2 | semidirect |
| 83. C193 | #536 | semidirect |
| 94. C22⋊Q8 | D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690555 | 2 |
| C2×Q8×D193 | 2 |
| #20259898 | 2 |
| #20259885 | 2 |
| #20259884 | 2 |
| #20259881 | 2 |
| #20259879 | 2 |
| #20259878 | 2 |
| #20259875 | 2 |
| #20259857 | 2 |
| C22⋊Q8×C193 | 2 |
| #536 | 193 |