Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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×C4⋊#11715895 | C2 | semidirect |
| 3. C2×#15690731 | C2 | semidirect |
| 4. C2×#15690730 | C2 | semidirect |
| 5. #20260637 | C2 | semidirect |
| 6. #20260497 | C2 | semidirect |
| 7. #390×C97 | C2 | semidirect |
| 88. C2×C4×C97 | D8 | semidirect |
| 143. C97 | #2054 | semidirect |
| 149. #390 | D97 | semidirect |
| 238. C2×C4 | #13095496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095496 | 2 |
| C2×C4⋊#11715895 | 2 |
| C2×#15690731 | 2 |
| C2×#15690730 | 2 |
| #20260637 | 2 |
| #20260497 | 2 |
| #390×C97 | 2 |
| #2054 | 97 |