Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
680 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 469 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 |
|---|---|---|
| 3. C2×#15690720 | C2 | direct (N × H) |
| 6. C22×#11715895 | C4 | semidirect |
| 10. #15690720 | C22 | direct (N × H) |
| 12. C22×C8×C97 | C4 | semidirect |
| 16. C2×#11715895 | C2×C4 | semidirect |
| 25. C2×C8×C97 | C2×C4 | semidirect |
| 37. C8×C97 | C22×C4 | semidirect |
| 38. #11715895 | C22×C4 | semidirect |
| 39. C22×C97 | #97 | semidirect |
| 47. C2×C97 | C2×#97 | semidirect |
| 51. C97 | C22×#97 | semidirect |
| 60. C22×C8 | Dic97 | semidirect |
| 74. C2×C8 | C2×Dic97 | semidirect |
| 89. C8 | C22×Dic97 | semidirect |
| 90. C22 | #15690720 | direct (N × H) |
| 98. C2 | C2×#15690720 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11715895 | 2 |
| C22×C4×Dic97 | 2 |
| C2×#15690720 | 2 |
| C23×C8×C97 | 2 |
| C22×#97 | 97 |