Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
456 conjugacy classes of subgroups; only the 305 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 305 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 | semidirect |
| 2. D4×#11715895 | C2 | semidirect |
| 3. #20260788 | C2 | semidirect |
| 4. C2×C4×#11715895 | C2 | semidirect |
| 22. #41×C97 | C8 | semidirect |
| 36. Q8×C97 | C2×C8 | semidirect |
| 37. D4×C97 | C2×C8 | semidirect |
| 40. C2×C4×C97 | C2×C8 | semidirect |
| 48. #11715895 | #41 | direct (N × H) |
| 64. C97 | C8×#41 | semidirect |
| 83. #41 | #11715895 | direct (N × H) |
| 100. Q8 | C2×#11715895 | semidirect |
| 101. D4 | C2×#11715895 | semidirect |
| 104. C2×C4 | C2×#11715895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11715895 | 2 |
| D4×#11715895 | 2 |
| #20260788 | 2 |
| C2×C4×#11715895 | 2 |
| C4×#41×C97 | 2 |
| C8×#41 | 97 |