Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
670 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#15690725 | C2 | semidirect |
| 2. #20260615 | C2 | semidirect |
| 4. C23×Dic97 | C22 | semidirect |
| 6. C2×C22⋊Dic97 | C22 | semidirect |
| 10. H(5,𝔽2)×C97 | C4 | semidirect |
| 43. C23×C97 | C22⋊C4 | semidirect |
| 54. C2×C4×C97 | C22⋊C4 | semidirect |
| 84. C97 | #1790 | semidirect |
| 89. H(5,𝔽2) | Dic97 | semidirect |
| 127. C23 | C22⋊Dic97 | semidirect |
| 144. C2×C4 | C22⋊Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690725 | 2 |
| #20260615 | 2 |
| C2×H(5,𝔽2)×C97 | 2 |
| #1790 | 97 |