Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
528 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 215 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. #20261848 | C2 | direct (N × H) |
| 2. C2×C4⋊#11715906 | C2 | semidirect |
| 4. C2×C4×#11715906 | C2 | semidirect |
| 7. C4⋊#11715906 | C22 | semidirect |
| 9. C4×#11715906 | C22 | semidirect |
| 37. C22×Dic97 | C8 | semidirect |
| 38. C2×C4×D97 | C8 | semidirect |
| 39. C2×C4×D97 | C8 | semidirect |
| 40. C2×C4×D97 | C8 | semidirect |
| 44. C22×C4×C97 | C8 | semidirect |
| 67. C2×C4×C97 | C2×C8 | semidirect |
| 70. C2×Dic97 | C2×C8 | semidirect |
| 73. C4×D97 | C2×C8 | semidirect |
| 74. C4×D97 | C2×C8 | semidirect |
| 99. C2×C97 | #431 | semidirect |
| 102. D97 | #431 | semidirect |
| 106. C97 | C2×#431 | semidirect |
| 142. C22×C4 | #11715906 | semidirect |
| 181. C2×C4 | C2×#11715906 | semidirect |
| 209. C2 | #20261848 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261848 | 2 |
| C2×C4⋊#11715906 | 2 |
| C2×C22⋊#11715906 | 2 |
| C2×C4×#11715906 | 2 |
| C22×C4×#87604 | 2 |
| C2×#431 | 97 |