Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
456 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
| 2. D4×#11715906 | C2 | semidirect |
| 3. #20261848 | C2 | semidirect |
| 4. C2×C4×#11715906 | C2 | semidirect |
| 31. #13095512 | C8 | semidirect |
| 32. #13095511 | C8 | semidirect |
| 33. #13095510 | C8 | semidirect |
| 37. #41×C97 | C8 | semidirect |
| 46. #11715906 | #41 | direct (N × H) |
| 47. Q8×C97 | C2×C8 | semidirect |
| 48. D4×C97 | C2×C8 | semidirect |
| 49. C2×C4×C97 | C2×C8 | semidirect |
| 50. C22⋊D97 | C2×C8 | semidirect |
| 51. C2×Dic97 | C2×C8 | semidirect |
| 52. D388 | C2×C8 | semidirect |
| 53. C4×D97 | C2×C8 | semidirect |
| 54. C4×D97 | C2×C8 | semidirect |
| 57. Dic194 | C2×C8 | semidirect |
| 77. C97 | C8×#41 | semidirect |
| 99. #41 | #11715906 | direct (N × H) |
| 117. Q8 | C2×#11715906 | semidirect |
| 120. D4 | C2×#11715906 | semidirect |
| 132. C2×C4 | C2×#11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11715906 | 2 |
| D4×#11715906 | 2 |
| #20261848 | 2 |
| C2×C4×#11715906 | 2 |
| #41×#87604 | 2 |
| C8×#41 | 97 |