Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
394 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 179 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. #20260786 | C2 | semidirect |
| 6. #20260757 | C2 | semidirect |
| 7. C8×Q8×C97 | C2 | semidirect |
| 43. Q8×C97 | M16 | semidirect |
| 75. C97 | #2991 | semidirect |
| 78. C8×Q8 | D97 | semidirect |
| 118. Q8 | #13095494 | 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 |
| #20260786 | 2 |
| #20260757 | 2 |
| C8×Q8×C97 | 2 |
| #2991 | 97 |