Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 119 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×C4×#11715906 | C2 | semidirect |
| 4. (C2×#11715906)⋊C4 | C2 | semidirect |
| 7. C22×#11715906 | C4 | semidirect |
| 11. C22⋊#11715906 | C4 | semidirect |
| 33. C22⋊#87604 | C8 | semidirect |
| 38. C22⋊Dic97 | C8 | semidirect |
| 39. #13095488 | C8 | semidirect |
| 40. C22⋊C4×C97 | C8 | semidirect |
| 55. C2×#87604 | C2×C8 | semidirect |
| 62. #11715906 | C22⋊C4 | direct (N × H) |
| 63. C2×C4×C97 | C2×C8 | semidirect |
| 64. C2×Dic97 | C2×C8 | semidirect |
| 68. C22×C97 | C4×C8 | semidirect |
| 74. C2×D97 | C4×C8 | semidirect |
| 94. C97 | C8×C22⋊C4 | semidirect |
| 132. C22⋊C4 | #11715906 | direct (N × H) |
| 157. C2×C4 | C2×#11715906 | semidirect |
| 171. C22 | C4×#11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11715906 | 2 |
| C2×C22⋊#11715906 | 2 |
| C2×C4×#11715906 | 2 |
| (C2×#11715906)⋊C4 | 2 |
| C22⋊C4×#87604 | 2 |
| C8×C22⋊C4 | 97 |