Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
440 conjugacy classes of subgroups; only the 333 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 333 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×#11715895 | C2 | direct (N × H) |
| 15. C2×#11715895 | Q8 | direct (N × H) |
| 18. C2×Q8×C97 | C8 | semidirect |
| 27. Q8×C97 | C2×C8 | semidirect |
| 37. #11715895 | C2×Q8 | direct (N × H) |
| 47. C2×C97 | C8×Q8 | semidirect |
| 52. C97 | C2×C8×Q8 | semidirect |
| 66. C2×Q8 | #11715895 | direct (N × H) |
| 79. Q8 | C2×#11715895 | direct (N × H) |
| 99. C2 | Q8×#11715895 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11715895 | 2 |
| C2×C4⋊#11715895 | 2 |
| C2×C4×#11715895 | 2 |
| C2×C4×Q8×C97 | 2 |
| C2×C8×Q8 | 97 |