Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 2. C2×#15690545 | C2 | semidirect |
| 3. C2×#15690542 | C2 | semidirect |
| 4. #20259822 | C2 | semidirect |
| 5. #20259819 | C2 | semidirect |
| 6. C22⋊#13095393 | C2 | semidirect |
| 7. C22⋊Q8×C193 | C2 | semidirect |
| 60. C193 | #452 | semidirect |
| 65. 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×#15690545 | 2 |
| C2×#15690542 | 2 |
| #20259822 | 2 |
| #20259819 | 2 |
| C22⋊#13095393 | 2 |
| C22⋊Q8×C193 | 2 |
| #452 | 193 |