Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#15690542 | C2 | semidirect |
| 2. C2×#15690539 | C2 | semidirect |
| 4. #20259832 | C2 | semidirect |
| 5. #20259823 | C2 | semidirect |
| 6. #20259819 | C2 | semidirect |
| 7. C22⋊Q8×C193 | C2 | semidirect |
| 27. #13095393 | D4 | semidirect |
| 55. C193 | #468 | semidirect |
| 59. C22⋊Q8 | D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690542 | 2 |
| C2×#15690539 | 2 |
| #20259873 | 2 |
| #20259832 | 2 |
| #20259823 | 2 |
| #20259819 | 2 |
| C22⋊Q8×C193 | 2 |
| #468 | 193 |