Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
402 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 183 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. Q8×#11715895 | C2 | semidirect |
| 3. #20260814 | C2 | semidirect |
| 4. #20260812 | C2 | semidirect |
| 5. #20260791 | C2 | semidirect |
| 6. C4×#13095494 | C2 | semidirect |
| 7. C8×Q8×C97 | C2 | semidirect |
| 44. Q8×C97 | M16 | semidirect |
| 57. C8×C97 | #41 | semidirect |
| 59. #11715895 | #41 | semidirect |
| 76. C97 | #2971 | semidirect |
| 79. C8×Q8 | D97 | semidirect |
| 120. Q8 | #13095494 | semidirect |
| 135. C8 | #13095512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095512 | 2 |
| Q8×#11715895 | 2 |
| #20260814 | 2 |
| #20260812 | 2 |
| #20260791 | 2 |
| C4×#13095494 | 2 |
| C8×Q8×C97 | 2 |
| #2971 | 97 |