Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
264 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20260786 | C2 | semidirect |
| 3. C4⋊C8×D97 | C2 | semidirect |
| 4. Q8⋊#11715895 | C2 | semidirect |
| 5. #20260464 | C2 | semidirect |
| 6. #20260462 | C2 | semidirect |
| 7. Q8⋊C8×C97 | C2 | semidirect |
| 28. #13095512 | C8 | semidirect |
| 60. Q8×C97 | C2×C8 | semidirect |
| 72. D388 | C2×C8 | semidirect |
| 110. C97 | #1477 | semidirect |
| 115. Q8⋊C8 | D97 | semidirect |
| 170. Q8 | C8×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095512 | 2 |
| #20260786 | 2 |
| C4⋊C8×D97 | 2 |
| Q8⋊#11715895 | 2 |
| #20260464 | 2 |
| #20260462 | 2 |
| Q8⋊C8×C97 | 2 |
| #1477 | 97 |