Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
166 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. Q8×#11715895 | C2 | semidirect |
| 4. #20260485 | C2 | semidirect |
| 6. #20260457 | C2 | semidirect |
| 7. Q8⋊C8×C97 | C2 | semidirect |
| 43. Q8×C97 | M16 | semidirect |
| 60. #11715895 | SD16 | semidirect |
| 78. C97 | #1583 | semidirect |
| 83. Q8⋊C8 | D97 | semidirect |
| 121. Q8 | #13095494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11715895 | 2 |
| C4×#13095498 | 2 |
| #20260812 | 2 |
| #20260485 | 2 |
| #20260464 | 2 |
| #20260457 | 2 |
| Q8⋊C8×C97 | 2 |
| #1583 | 97 |