Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
370 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20261464 | C2 | semidirect |
| 2. #20261087 | C2 | semidirect |
| 3. #20261017 | C2 | semidirect |
| 5. Q8×#11715895 | C2 | semidirect |
| 45. Q8×C97 | SD16 | semidirect |
| 75. C97 | #3359 | semidirect |
| 122. Q8 | #13095499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261464 | 2 |
| #20261087 | 2 |
| #20261017 | 2 |
| #20260940 | 2 |
| Q8×#11715895 | 2 |
| C4×#13095499 | 2 |
| D4×Q8×C97 | 2 |
| #3359 | 97 |