Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
180 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 59 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×#11715906 | C2 | semidirect |
| 3. #20261824 | C2 | semidirect |
| 4. Q8⋊#11715906 | C2 | semidirect |
| 6. C8×#11715906 | C2 | semidirect |
| 39. #13095500 | C8 | semidirect |
| 40. #13095499 | C8 | semidirect |
| 41. #13095498 | C8 | semidirect |
| 43. SD16×C97 | C8 | semidirect |
| 55. #11715906 | SD16 | direct (N × H) |
| 56. Q8×C97 | C2×C8 | semidirect |
| 63. Dic194 | C2×C8 | semidirect |
| 65. C8×C97 | C2×C8 | semidirect |
| 66. #11715895 | C2×C8 | semidirect |
| 87. C97 | C8×SD16 | semidirect |
| 116. SD16 | #11715906 | direct (N × H) |
| 134. Q8 | C2×#11715906 | semidirect |
| 153. C8 | C2×#11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11715906 | 2 |
| D4×#11715906 | 2 |
| #20261824 | 2 |
| Q8⋊#11715906 | 2 |
| D4⋊#11715906 | 2 |
| C8×#11715906 | 2 |
| SD16×#87604 | 2 |
| C8×SD16 | 97 |