Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
176 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 72 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×#11715897 | C2 | semidirect |
| 3. #20261598 | C2 | semidirect |
| 4. Q8⋊#11715897 | C2 | semidirect |
| 6. #20261576 | C2 | semidirect |
| 39. SD16×C97 | C8 | semidirect |
| 43. Q8×C97 | C2×C8 | semidirect |
| 59. C8×C97 | C2×C8 | semidirect |
| 78. C97 | SD16⋊C8 | semidirect |
| 104. SD16 | #11715897 | semidirect |
| 121. Q8 | C2×#11715897 | semidirect |
| 138. C8 | C2×#11715897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11715897 | 2 |
| D4×#11715897 | 2 |
| #20261598 | 2 |
| Q8⋊#11715897 | 2 |
| D4⋊#11715897 | 2 |
| #20261576 | 2 |
| SD16×Dic97 | 2 |
| SD16⋊C8 | 97 |