Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
848 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 125 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×#15690732 | C2 | semidirect |
| 3. C2×#15690731 | C2 | semidirect |
| 4. C2×#15690730 | C2 | semidirect |
| 5. C2×#15690722 | C2 | semidirect |
| 6. #20260592 | C2 | semidirect |
| 7. C2×#102×C97 | C2 | semidirect |
| 16. C2×D4×D97 | C4 | semidirect |
| 18. C22×#11715895 | C22 | semidirect |
| 19. C2×C4⋊Dic97 | C22 | semidirect |
| 27. C22×C8×C97 | C22 | semidirect |
| 28. C2×C4⋊C4×C97 | C22 | semidirect |
| 112. D4×C97 | C22⋊C4 | semidirect |
| 132. D388 | C22⋊C4 | semidirect |
| 167. C2×D97 | #102 | semidirect |
| 186. C97 | #1786 | semidirect |
| 191. C2×#102 | D97 | semidirect |
| 206. C22×C8 | C2×D97 | semidirect |
| 208. C2×C4⋊C4 | C2×D97 | semidirect |
| 303. D4 | #13095488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D97 | 2 |
| C2×#15690732 | 2 |
| C2×#15690731 | 2 |
| C2×#15690730 | 2 |
| C2×#15690722 | 2 |
| #20260592 | 2 |
| C2×#102×C97 | 2 |
| #1786 | 97 |