Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
154 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 67 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×#15690539 | C2 | semidirect |
| 2. #20259858 | C2 | semidirect |
| 3. #20259826 | C2 | semidirect |
| 6. #15690539 | C22 | semidirect |
| 10. C4×Dic193 | C22 | semidirect |
| 13. #41×C193 | C4 | semidirect |
| 15. C2×Q8×C193 | C4 | semidirect |
| 17. C2×D4×C193 | C4 | semidirect |
| 56. C193 | #421 | semidirect |
| 64. #41 | Dic193 | semidirect |
| 66. C2×Q8 | Dic193 | semidirect |
| 68. C2×D4 | Dic193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690539 | 2 |
| #20259858 | 2 |
| #20259826 | 2 |
| C2×#41×C193 | 2 |
| #421 | 193 |