Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
456 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 225 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 |
|---|---|---|
| 2. Q8×#11715895 | C2 | semidirect |
| 3. C8×D388 | C2 | semidirect |
| 4. #20260800 | C2 | semidirect |
| 5. #20260787 | C2 | semidirect |
| 6. C4×C8×D97 | C2 | semidirect |
| 7. C8×Q8×C97 | C2 | semidirect |
| 24. #13095512 | C8 | direct (N × H) |
| 44. Q8×C97 | C2×C8 | semidirect |
| 51. D388 | C2×C8 | semidirect |
| 55. C4×D97 | C2×C8 | semidirect |
| 57. C8×C97 | #41 | semidirect |
| 59. #11715895 | #41 | semidirect |
| 76. C97 | C8×#41 | semidirect |
| 79. C8×Q8 | D97 | semidirect |
| 120. Q8 | C8×D97 | semidirect |
| 135. C8 | #13095512 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095512 | 2 |
| Q8×#11715895 | 2 |
| C8×D388 | 2 |
| #20260800 | 2 |
| #20260787 | 2 |
| C4×C8×D97 | 2 |
| C8×Q8×C97 | 2 |
| C8×#41 | 97 |