Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
280 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 7. #15690878 | C4 | direct (N × H) |
| 12. C4×#11715895 | C4 | semidirect |
| 13. C8×Dic97 | C4 | semidirect |
| 14. C8×Dic97 | C4 | semidirect |
| 15. C4×C8×C97 | C4 | semidirect |
| 48. C8×C97 | C42 | semidirect |
| 50. #11715895 | C42 | semidirect |
| 57. C4×C97 | #106 | semidirect |
| 61. Dic97 | #106 | semidirect |
| 68. C97 | C4×#106 | semidirect |
| 82. C4×C8 | #87604 | semidirect |
| 118. C8 | C4×#87604 | semidirect |
| 128. C4 | #15690878 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690878 | 2 |
| C4×C4⋊#87604 | 2 |
| #20261609 | 2 |
| C4×C8×D97 | 2 |
| C4×#106 | 97 |