Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
316 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 6. C4⋊#11715906 | C4 | direct (N × H) |
| 25. C4×#87604 | C8 | semidirect |
| 32. C4×Dic97 | C8 | semidirect |
| 33. C4×Dic97 | C8 | semidirect |
| 34. C4×Dic97 | C8 | semidirect |
| 35. C42×C97 | C8 | semidirect |
| 72. #87604 | C4⋊C8 | semidirect |
| 76. C4×C97 | C4×C8 | semidirect |
| 77. C4×C97 | C4⋊C8 | semidirect |
| 79. Dic97 | C4×C8 | semidirect |
| 80. Dic97 | C4⋊C8 | semidirect |
| 89. C97 | C4×C4⋊C8 | semidirect |
| 124. C42 | #11715906 | semidirect |
| 168. C4 | C4×#11715906 | semidirect |
| 169. C4 | C4⋊#11715906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11715906 | 2 |
| C2×C4×#11715906 | 2 |
| (C2×#11715906)⋊C4 | 2 |
| C42×#87604 | 2 |
| C4×C4⋊C8 | 97 |