Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
440 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 228 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. #20261784 | C2 | semidirect |
| 2. Q8×#11715897 | C2 | semidirect |
| 20. #13095519 | Q8 | direct (N × H) |
| 24. Q8×D97 | C8 | semidirect |
| 37. Q8×C97 | C2×C8 | semidirect |
| 48. Dic194 | C2×C8 | semidirect |
| 50. #11715897 | C2×Q8 | semidirect |
| 65. D97 | C8×Q8 | semidirect |
| 67. C97 | C2×C8×Q8 | semidirect |
| 105. Q8 | #13095519 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261784 | 2 |
| Q8×#11715897 | 2 |
| #20261736 | 2 |
| C4×#13095519 | 2 |
| C4×Q8×D97 | 2 |
| C2×C8×Q8 | 97 |