Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
412 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 2. C4×C22⋊Dic97 | C2 | semidirect |
| 3. #20260502 | C2 | semidirect |
| 7. #15690725 | C4 | direct (N × H) |
| 10. C23×C4×C97 | C4 | semidirect |
| 14. C2×C4⋊C4×C97 | C4 | semidirect |
| 15. C2×C22⋊C4×C97 | C4 | semidirect |
| 17. C2×C42×C97 | C4 | semidirect |
| 20. C22⋊Dic97 | C2×C4 | semidirect |
| 49. C23×C97 | C42 | semidirect |
| 67. C2×C4×C97 | C42 | semidirect |
| 94. C4×C97 | #99 | semidirect |
| 104. C97 | C4×#99 | semidirect |
| 110. C23×C4 | Dic97 | semidirect |
| 114. C2×C4⋊C4 | Dic97 | semidirect |
| 116. C2×C22⋊C4 | Dic97 | semidirect |
| 119. C2×C42 | Dic97 | semidirect |
| 153. C23 | C4×Dic97 | semidirect |
| 174. C2×C4 | C4×Dic97 | semidirect |
| 199. C4 | #15690725 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690725 | 2 |
| C4×C22⋊Dic97 | 2 |
| #20260502 | 2 |
| C2×C4×D4×C97 | 2 |
| C4×#99 | 97 |