Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 105 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×#15690739 | C2 | semidirect |
| 3. C2×C22⋊#11715895 | C2 | semidirect |
| 4. C2×#15690722 | C2 | semidirect |
| 5. C2×#15690722 | C2 | semidirect |
| 6. C2×#15690720 | C2 | semidirect |
| 7. C2×C22⋊C8×C97 | C2 | semidirect |
| 45. C2×#11715895 | D4 | semidirect |
| 65. C2×C8×C97 | D4 | semidirect |
| 151. C97 | #1955 | semidirect |
| 157. C2×C22⋊C8 | D97 | semidirect |
| 211. C2×C8 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D97 | 2 |
| C2×#15690739 | 2 |
| C2×C22⋊#11715895 | 2 |
| C2×#15690722 | 2 |
| C2×#15690720 | 2 |
| C2×C22⋊C8×C97 | 2 |
| #1955 | 97 |