Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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×#15690743 | C2 | semidirect |
| 3. C2×#15690730 | C2 | semidirect |
| 4. C2×#15690730 | C2 | semidirect |
| 5. C2×C22⋊#11715895 | C2 | semidirect |
| 6. #20260497 | C2 | semidirect |
| 7. #380×C97 | C2 | semidirect |
| 41. C2×#11715895 | D4 | semidirect |
| 144. C97 | #2033 | semidirect |
| 150. #380 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690784 | 2 |
| C2×#15690743 | 2 |
| C2×#15690730 | 2 |
| C2×C22⋊#11715895 | 2 |
| #20260497 | 2 |
| #380×C97 | 2 |
| #2033 | 97 |