Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
396 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 191 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 |
| 18. C2×Dic194 | C8 | semidirect |
| 19. Q8×D97 | C8 | semidirect |
| 22. C2×Q8×C97 | C8 | semidirect |
| 52. C97 | #2982 | semidirect |
| 67. C2×Q8 | #11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11715906 | 2 |
| #20261848 | 2 |
| C2×Q8×#87604 | 2 |
| #2982 | 97 |