Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20259894 | C2 | semidirect |
| 2. #20259890 | C2 | semidirect |
| 3. #20259884 | C2 | semidirect |
| 4. #20259883 | C2 | semidirect |
| 5. #20259875 | C2 | semidirect |
| 7. #20259859 | C2 | semidirect |
| 8. C2×#15690534 | C2 | semidirect |
| 9. C22⋊Q8×C193 | C2 | semidirect |
| 66. C193 | #539 | semidirect |
| 73. C22⋊Q8 | D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259894 | 2 |
| #20259890 | 2 |
| #20259884 | 2 |
| #20259883 | 2 |
| #20259875 | 2 |
| #20259873 | 2 |
| #20259859 | 2 |
| C2×#15690534 | 2 |
| C22⋊Q8×C193 | 2 |
| #539 | 193 |